a company purchased a new computer system for $28,000. one year later, the resale value of the system was $15,700. assume that the value of the computer system declines according to an exponential model. At what rate was the value of the computer system changing 4 years after it was purchased?
A. Declining at the rate of $2,767.74 per year.
B. Declining at the rate of $1,601.26 per year.
C. Declining at the rate of $3,6214.88 per year.
D. Declining at the rate of $8,803.21 per year.
E. Declining at the rate of $2,546.52 per year.
F. None of the above.

Answers

Answer 1

The rate at which the value of the computer system is changing 4 years after it was purchased is "Declining at the rate of $8,803.21 per year". The correct option is D.

We can use the exponential decay formula \(V(t) = V0 * e^{-kt}\), where V(t) is the value of the computer system after t years, V0 is the initial value, and k is the decay rate.

We know that V(1) = $15,700 and V(0) = $28,000, so we can solve for k:

\($15,700 = $28,000 * e^{-k*1}\)

\(e^{-k} = 0.5607\)

-k = ln(0.5607) ≈ -0.5797

k ≈ 0.5797

Therefore, the decay rate is approximately 0.5797 per year.

To find the rate of change of the value of the computer system 4 years after it was purchased, we can take the derivative of V(t) with respect to t:

dV/dt = -k * V0 * \(e^{-kt}\)

Substituting t = 4, V0 = $28,000, and k ≈ 0.5797, we get:

dV/dt = -0.5797 * $28,000 * \(e^{-0.5797*4}\) ≈ -$8,803.21 per year

Therefore, the value of the computer system is declining at the rate of approximately $8,803.21 per year 4 years after it was purchased.

The correct answer is (D) Declining at the rate of $8,803.21 per year.

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Related Questions

what is the vertex of this graph?
Is the vertex a minimum or a maximum?

what is the vertex of this graph?Is the vertex a minimum or a maximum?

Answers

Answer:

Maximum

Step-by-step explanation:

Answer:

(-2, -3)

Maximum

Step-by-step explanation:

The vertex of a parabola is the highest or lowest point,

(-2, -3)

Maximum

let f{o) = 0, /(1) = 1, /(2) = 22 , /(3) = 333 = 327, etc. in general, f(n) is written as a stack n high, of n's as exponents. show that f is primitive recursive.

Answers

So,  g(n) is primitive recursive, as required.

In order to show that f is primitive recursive, we must first show that the function which outputs a stack n high of n's as exponents is primitive recursive.

Let's call this function g(n). Here's the definition:g(0) = 1g(n+1) = n ^ g(n)This can be translated into a recursive function using the successor and exponentiation functions:

g(0) = 1 g(n+1) = (n)^(g(n))

To show that g(n) is primitive recursive, we need to show that it can be constructed from the basic primitive recursive functions using composition, primitive recursion, and projection.

First, we'll need to define the basic primitive recursive functions.

Here's the list:

Successor: S(x) = x+1

Projection: pi_k^n(x1, ..., xn) = xk

Zero: Z(x) = 0

Here are the composition and primitive recursion rules:

Composition: If f: k_1 x ... x k_n -> m and g_1: m -> p_1 and ... and g_n:

m -> p_n are primitive recursive functions, then h:

k_1 x ... x k_n -> p_1 x ... x p_n defined by

h(x1, ..., xn) = (g_1(f(x1, ..., xn)), ..., g_n(f(x1, ..., xn)))

is a primitive recursive function.Primitive recursion:

If f: k_1 x ... x k_n x m -> m and

g: k_1 x ... x k_n -> m and

h: k_1 x ... x k_n x m x p -> p

are primitive recursive functions such that for all x1, ..., xn, we have f(x1, ..., xn, 0) = g(x1, ..., xn) and f(x1, ..., xn, m+1)

= h(x1, ..., xn, m, f(x1, ..., xn, m)), then k:

k_1 x ... x k_n x m -> m defined by k(x1, ..., xn, m) = f(x1, ..., xn, m) is a primitive recursive function.

Now we can show that g(n) is primitive recursive using these tools.

We'll use primitive recursion with base case Z(x) = 1 and recursive case f(n, g(n)). We define f as follows:

f(n, 0) = 1f(n, m+1)

=\(n ^ m\) (using the exponentiation function)

Then we define g(n) = f(n, n).

It's clear that g(n) is the same function we defined earlier, and that f(n, m) is primitive recursive.

Therefore, g(n) is primitive recursive, as required.

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g(n) is the same function we defined earlier, and that f(n, m) is primitive recursive. Therefore, g(n) is primitive recursive, as required.

In order to show that f is primitive recursive, we must first show that the function which outputs a stack n high of n's as exponents is primitive recursive.

Let's call this function g(n). Here's the definition: \(g(0) = 1g(n+1) = n ^ g(n)\).

This can be translated into a recursive function using the successor and exponentiation functions: \(g(0) = 1g(n+1) = n ^ g(n)\\\).

To show that g(n) is primitive recursive, we need to show that it can be constructed from the basic primitive recursive functions using composition, primitive recursion, and projection.

First, we'll need to define the basic primitive recursive functions. Here's the list:

Successor: S(x) = x+1

Projection: \(pi_k^n(x1, ..., xn) = xk\)

Zero: Z(x) = 0,

Here are the composition and primitive recursion rules:

Composition: If f: k_1 x ... x k_n -> m and g_1: m -> p_1 and ... and g_n: m -> p_n are primitive recursive functions,

then h: k_1 x ... x k_n -> p_1 x ... x p_n defined by

h(x1, ..., xn) = \((g_1(f(x1, ..., xn)), ..., g_n(f(x1, ..., xn)))\)is a primitive recursive function.

Primitive recursion: If f: k_1 x ... x k_n x m -> m and

g: k_1 x ... x k_n -> m and

h: k_1 x ... x k_n x m x p -> p are primitive recursive functions such that for all x1, ..., xn,

we have \(f(x1, ..., xn, 0) = g(x1, ..., xn)\)and \(f(x1, ..., xn, m+1) = h(x1, ..., xn, m, f(x1, ..., xn, m))\), then

k: k_1 x ... x k_n x m -> m defined by

k(x1, ..., xn, m) = f(x1, ..., xn, m) is a primitive recursive function.

Now we can show that g(n) is primitive recursive using these tools. We'll use primitive recursion with base case Z(x) = 1 and recursive case f(n, g(n)). We define f as follows: \(f(n, 0) = 1f(n, m+1) = n ^ m\) (using the exponentiation function).

Then we define g(n) = f(n, n).

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100 points!! The question and graph is provided with the attached image.

A. {a=2, b=3}
B. {a=3, b=2}
C. {a=−3, b=2}
D. {a=2, b=−3}

100 points!! The question and graph is provided with the attached image.A. {a=2, b=3}B. {a=3, b=2} C.

Answers

Answer:

b its b im pretty sure if not d  okk!!

16-2k=14. what is the value of k​

Answers

Answer:

k = 1

Step-by-step explanation:

16 - 2k = 14

- 16       - 16

    -2k = -2

     -2     -2

       k = 1

Subtract 16 on both sides. -2k = -2
Divide -2 on both sides. k = 1

35/48*100 fraction into percentage.​

Answers

Answer:

729167

Step-by-step explanation:

Now we can see that our fraction is 72.916666666667/100, which means that 35/48 as a percentage is 72.9167%.

television retails for $4,500. What is the purchase price in dollars of the television if it has been marked up 25% of the retail price

Answers

The purchase price in dollars of the television that has been marked up 25% of the retail price of $4,500 would be $5,625.

To find the purchase price of the television in dollars, follow these steps:

1. Determine the markup amount: 25% of the retail price ($4,500).
2. Subtract the markup amount from the retail price to find the purchase price.

Step 1: Calculate the markup amount:
25% of $4,500 = 0.25 × 4,500 = $1,125

Step 2: Subtract the markup amount from the retail price:
$4,500 (retail price) - $1,125 (markup) = $3,375

The purchase price of the television in dollars is $3,375.

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Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below.

Answers

the system can be explained in equation form as x - y =4, an (x + y)/2 = 18. Based on these equations, we can plus in numbers from the given answers and come up with a solution where both equations are satisfied. The two numbers that satisfy both equations are (20, 16).

Last month, a basketball team scored 83, 84, 85, 87, 89, 88, 67, 79, and 81 points in their games. Which data value(s) are outliers? Select all that apply.

Answers

The data value that is an outlier is 67

How to determine the outlier?

The dataset is given as:

83, 84, 85, 87, 89, 88, 67, 79, and 81

To determine the outlier, we select the data values that are relatively far from others

In the above dataset, the data element 67 is far from other data values

Hence, the data value that is an outlier is 67

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What is the first 5 terms for 40-3n

Answers

There is only 2 terms
Answer:   37, 34, 31, 28, 25

=================================================

Explanation:

The variable n represents the term number.

Plug n = 1 into the expression to get 40-3n = 40-3*1 = 37.

Therefore, 37 is the first term.

The second term is 34 because 40-3n = 40-3*2 = 34.

This process is repeated for values n = 3, n = 4, and n = 5. You should get 31, 28, and 25 for the third, fourth, and fifth terms in that order.

--------

An alternative is to subtract 3 from each term to get the next term.

37-3 = 3434-3 = 3131-3 = 2828-3 = 25

This alternative method will only be useful once you find the first term is 37.

Which polynomial is in standard form?

Which polynomial is in standard form?

Answers

B:
Explanation that equation is the B

If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420, find the principal​

Answers

As per the given simple interest, the principal amount is $165.35.

The term simple interest in math is defined as  the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.

Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.

Therefore, through the given question we have identified the value of

interest rate = 3.5%

time period = 44

sum amount = 420.

Then the principal amount is calculated by using the formula of simple interest as,

P = A / (1 + rt)

Here first we have to convert R percent to r a decimal, then we get

r = R/100 = 3.5%/100 = 0.035 per year.

Now, we have to apply the values on the equation and then we have to solve our equation, then we get

P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866

P = $165.35

Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.

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7. -4y = 48 what is the answer for y? To get 48

Answers

Answer:

Y= -12

Step-by-step explanation:

to get the answer to Y you just have to divided the number beside the variable to get just one itself.

so divide both sides by -4 to get

y=-12

Answer:

-12 lol I just got out of school and we did this exact type of math

Step-by-step explanation:

Let's say you have this data: 25, 26, 24, 26, 25, 7, 8, 8, 15, 10, 25, 24, 26 What should your bin size be if you want to have 10 bins

Answers

Your bin size should be 2

are the fractions 2/2 and 8/8 equivalent fractions​?

Answers

Answer:

Yes

Step-by-step explanation:

2/2 can be simplified to 1. 8/8 can be simplified to 1. 1=1 so the fractions are equivalent.

Answer:

Yes

Step-by-step explanation:

2 is the same as 2 so it equals 1 same thing with 8/8because 8=8 and one and one are the same thing

This is long and complex, may you please get some help?

This is long and complex, may you please get some help?

Answers

Answer:

Step-by-step explanation:

a = -4 , b = 16 and c = -17

\(x =\dfrac{-b}{2a}\\\\x = \dfrac{-16}{2*(-4)}\\\\\\ =\dfrac{-16}{-8}\\\\\\\\\)

x = 2

y = -4(2)² + 16*2 - 17

   = -4*4 + 32 - 17

   = -16 + 32 - 17

y = -1

Vertex (2, -1)

axis of symmetry: x = 2

The average third grade student can read
80 words in 5 minutes. What is the average
reading rate per minute?
write an expression to represent the problem.

Answers

Answer:

16x

Step-by-step explanation:

80 divided by 5 is 16, so the student can read 16 words per minute. X is the number of minutes.

The average reading rate per minute is 16 words/ min.

and its expression will be \(16x\)  

where, \(x\) represents the minutes

What is proportion ?

A proportion is an equation based on the equality of two ratios.

It is given that the average third grade student can read 80 words in 5 minutes and it is to calculate the average words read by the student per minute :

\(\begin{aligned}5 \text{\:min}&\rightarrow 80 \text{\:words}\\1 \text{\:min}&\rightarrow \frac{80}{5}\text{\:words} \\&\rightarrow 16 \text{\:words}\end{aligned}\)

Therefore, the average reading rate per minute is 16 words/ min.

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Write a statement and reason proof. Number each statement and each reason. Give the line numbers of the lines used to determine which lines were used to arrive at each conclusion. Let A= apples are red C= cherries are black M= melons are yellow P= peaches are ripe. S= strawberries are sweet The following premises are given to be true. Either strawberries are sweet or melons are not yellow. If peaches are ripe and strawberries are sweet then apples are not red. Apples are red. Peaches are ripe. PROVE: Melons are not yellow.

Answers

Melons are not yellow due to the given premises and logical deductions.This is the statement and the proof.

Either strawberries are sweet or melons are not yellow. (Premise)

If peaches are ripe and strawberries are sweet, then apples are not red. (Premise)

Apples are red. (Premise)

Peaches are ripe. (Premise)

Assume that melons are yellow (for contradiction).

Since melons are yellow and apples are red, the statement "If peaches are ripe and strawberries are sweet, then apples are not red" is false, contradicting premise 2.

Therefore, our assumption that melons are yellow is false, and hence, melons are not yellow. (Contradiction)

Thus, we have proven that melons are not yellow.

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Answer these correct and ill give 500 pts!!
1. Agricultural policy made it cheaper for Americans to buy food that can be bad for our health.

False
True
2. Which option identifies the concept represented in the following scenario?
A rural cherry-growing co-op in northern Michigan contracts with a company in Wisconsin to process dried cherries.

vertical integration
monocropping
sustainability
horizontal consolidation
3. Which option identifies the agency most likely to be involved in monitoring in the following scenario?
Forest fires have caused contamination of a river in southern Colorado. Fish from the river are found to contain high levels of mercury.

Food and Drug Administration
Environmental Protection Agency
Department of Agriculture
Forest Service

Answers

Answer:

ture

Step-by-step explanation:

Answer:

1.True

2.Monocropping

3.Food and Drug administration

Step-by-step explanation:

explain, giving two reasons,when a person is entitled to claim for UIF benefits ​

Answers

Two reasons when a person is entitled too access the Unemployed Insurance Fund are:

When a worker becomes unemployed within 6 months of losing their job.Dependents of a deceased contributor.

What is the Unemployed Insurance Fund (UIF)?

The unemployed insurance fund (UIF) is described as a short-term relief given to workers who are unable to work or when they become unemployed due to several reasons. In addition, the fund (UIF), can also be accessed by dependents of a deceased contributor.

Therefore, two reasons when a person is entitled too access the Unemployed Insurance Fund are:

When a worker becomes unemployed within 6 months of losing their job.Dependents of a deceased contributor.

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NEED ASAP . 19 MINUTES LEFT GIVNG BRAINLIEST PLZZZZ

NEED ASAP . 19 MINUTES LEFT GIVNG BRAINLIEST PLZZZZ

Answers

Answer:

9

Step-by-step explanation:

so sorry if im too late...

Type the correct answer in the box. Round off your answer to the nearest integer.
ZA and ZC are right angles. mZp=
D
6
A
degrees.
P
5
C
B

Type the correct answer in the box. Round off your answer to the nearest integer.ZA and ZC are right

Answers

Answer:

59°

Step-by-step explanation:

in ∆abd according to Pythagorean theorem:

(bd)²=√(ad)²+(ab)²

= √25+36

= 61

abcd. cosld= cd/bd

=4/√61

= 61. _~0.512

so lp = arc cos 0.512

_~59°

What is the simplest form of 8(5k+7)−10(6k−7)

Answers

The simplest form of the given expression is -20k + 126.

To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
  8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
  40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
  (40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
  -20k + 126
The simplest form of the given expression is -20k + 126.

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reflect the point worksheet

Answers

Answer:

I don't know the answer I think

A cone-shaped container has a height of 240 in. And a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week. How many weeks will it take for all of the chemical to evaporate? use 3. 14 to approximate pi. Enter your answer in the box.

Answers

Therefore, it will take approximately 1415.7 weeks for all of the chemical to evaporate.

To calculate the volume of a cone, we can use the formula:

\(Volume = (1/3) * π * r^2 * h\)

Given that the height (h) of the cone is 240 inches and the radius (r) is 150 inches, we can substitute these values into the formula:

\(Volume = (1/3) * 3.14 * 150^2 * 240\)

Simplifying the equation:

Volume = 3.14 * 22500 * 240

Volume ≈ 16988400 cubic inches

Now, we know that the liquid chemical evaporates at a rate of 12,000 cubic inches per week. To find out how many weeks it will take for all the chemical to evaporate, we can divide the total volume of the chemical by the evaporation rate:

Number of weeks = Volume / Evaporation rate

Number of weeks = 16988400 / 12000

Number of weeks ≈ 1415.7 weeks

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simplify the expression x · ¡ [x > 0] − [x < 0] ¢ .

Answers

Putting it all together, we have:

- If x is greater than 0, then [x > 0] is 1 and [x < 0] is 0, so the expression becomes x · ¡0¢, which simplifies to x · 1, or simply x.

- If x is less than 0, then [x > 0] is 0 and [x < 0] is 1, so the expression becomes x · ¡1¢, which simplifies to x · (-1), or -x.

- If x is equal to 0, then both [x > 0] and [x < 0] are 0, so the expression becomes x · ¡0¢, which simplifies to 0.

Therefore, the simplified expression is:

x · ¡ [x > 0] − [x < 0] ¢  = { x, if x > 0; -x, if x < 0; 0, if x = 0 }

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What type of graph is this

What type of graph is this

Answers

Answer:

Its a graph to find out the median. Or can be called a box plot

Step-by-step explanation:

Mr. Martinez is buying food for a party. Hamburger patties are sold in packages of 6 and hamburger buns are sold in packages of 8. If he wants to have an equal number of each, what is the LEAST number of hamburger patties and buns that Mr. Martinez will have to buy?

Enter the correct answer in the box.

Answers

Answer:

24 is the least number of hamburger patties and buns Mr. Martinez will have to buy.

Step-by-step explanation:

You need to find the LCM of 6 and 8. The number they have first have common is 24

simplify the following

\( \frac{5 {ab } ^{2} + 10 {a}^{4} {b}^{3} - 15 {ab}^{3} }{5ab} \)

Answers

Ur welcome workings down below
simplify the following[tex] \frac{5 {ab } ^{2} + 10 {a}^{4} {b}^{3} - 15 {ab}^{3} }{5ab} [/tex]

Scale Factor: 1/2; Center: point N

Scale Factor: 1/2; Center: point N

Answers

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

What is the new coordinate of points of M and O?

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f(t)=475(0.5)t. Evaluate the function when t=3. Round your answer to the nearest tenth.

Answers

The function when t=3 to the nearest tenth is 59.4.

How did we get the value?

The initial amount is a = 475, and the rate of decay r is 50%.

To evaluate the function when t=3, we plug in t=3:

f(3) = 475(0.5)^3 = 475 * (0.125) = 59.375

Rounding to the nearest tenth, f(3) = 59.4.

Therefore, the correct answer is as given above. It could be concluded that the rounded answer to the nearest tenth is 59.4

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The __ root and horns receive __ signals, while the __ root and horns project __ signals.a - ventral, efferent. dorsal, afferent.b - dorsal, efferent. ventral, afferentc - dorsal, afferent. ventral, efferent.d - ventral, afferent. dorsal, efferent. matching: 1 . share a place where financial securities are bought and sold 2 . industrial revolution the largest of all american stock exchanges, created in 1792 3 . new york stock exchange started in the mid-19th century; financial emphasis moved from farming to the factory 4 . american stock exchange the formal name of the curb traders; it began in 1908 5 . stock exchange a unit of the equal parts of the capital stock divided by a corporation A building supply has two locations in town. The office receives orders from two of its best customers, each requiring 3/4-inch drywall board to be delivered. Customer A needs at least one hundred sheets delivered and Customer B needs at least one hundred-forty sheets delivered. Deliveries can be sent from either of the supply companies' warehouses. The warehouse on the north side of town has one hundred-sixty sheets in stock; the south-side warehouse has ninety sheets in stock. Delivery costs per sheet are as follows: $1. 50/board from the northern warehouse to Customer A,$1. 20/board from the northern warehouse to Customer B, $0. 80/board from the southern warehouse to Customer A, and $1. 10/board from the southern warehouse to Customer. 1. Find the shipping arrangement which minimizes costs. 2. What will be the minimum cost?3. Will there be any product left in either warehouse after fulfilling the orders? Current Liabilities and Ratios Several accounts that appeared on Kruse's 2017 balance sheet are as follows: Accounts Payable $55,000 Equipment $950,000 Marketable Securities 40,000 Taxes Payable 15,000 Accounts Receivable 180,000 Retained Earnings 250,000 Notes Payable, 12%, due in 60 days 20,000 Inventory 85,000 Capital Stock 1,150,000 Allowance for Doubtful Accounts 20,000 Salaries Payable 10,000 Land 600,000 Cash 15,000 Required: 1. Prepare the Current Liabilities section of Kruse's 2017 balance sheet. Kruse Partial Balance Sheet As Of December 31, 2017 Current liabilities: Accounts payable $ 55,000 Notes payable, 12%, due in 60 days 20,000 Taxes payable 15,000 Salaries payable 10,000 Total current liabilities $ 100,000 Feedback Prepare the liabilities section of the balance sheet. 2. Compute Kruse's working capital. __ 3. Compute Kruse's current ratio. __: 1 10) When Perry Person got a paycheck, Perry went shopping. He spent $26 on a shirt and twice as much on jeans. Then he spent half of what he had left on a snack. On his way home, he found $10 and ended up with $ 24. How much was Perry's paycheck ? prior to the 1990s, which of the following was the primary form of agency in the real estate industry? Suppose that the nation of Micronesia decides to participate in the international trade of timber. 1. Shift the line representing the world price in a way that results in Micronesia exporting timber. 2. Adjust the shaded area so that it correctly represents producer surplus for Micronesia\'s firms once the country is open to international trade. winter sports apparel issued convertible debt securities. which of the following statements is true regarding their journal entries as a result of this issuance? the teapot dome political scandal of president harding's administration resulted in the conviction and imprisonment of his secretary of ____ Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0t38Step 1 of 2:What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.Step 2 of 2:What is the average waiting time?