A car with an initial cost of $23,000 is decreasing in value at a rate of 8% each year. Write the exponential decay function described in this situation. Then use your function to determine when the value of the car will be $15,000, to the nearest year.

Question

Mathematics

Hendrix

20 October, 12:28

A car with an initial cost of $23,000 is decreasing in value at a rate of 8% each year. Write the exponential decay function described in this situation. Then use your function to determine when the value of the car will be $15,000, to the nearest year.

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Answers (1)

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Gabby · Answer 1

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P (1 - r/n) ^ nt

Where

A represents the value after t years.

n represents the period for which the decrease in value is calculated

t represents the number of years.

P represents the value population.

r represents rate of decrease.

From the information given,

P = 23000

r = 8% = 8/100 = 0.08

n = 1

Therefore, the exponential decay function described in this situation is

A = 23000 (1 - 0.08/n) 1) ^ 1 * t

A = 23000 (0.92) ^t

If A = 15000, then

15000 = 23000 (0.92) ^t

0.92^t = 15000/23000 = 0.6522

Taking log of both sides to base 10

Log 0.92^t = log 0.6522

tlog 0.92 = log 0.6522

- 0.036t = - 0.1856

t = - 0.1856 / - 0.036

t = 5 years to the nearest year