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Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation 2000=16000(1−r)^t represents the situation, where t is the age of the car in years and r is the rate of depreciation. Solve for the age of Devon's car? Use a calculator and round your answer to the nearest whole number.

Verified Answer :

Given:
initial value = 16,000
depreciation rate = 35%
current value = 2,000

equation:
2,000 = 16,000 (1-r)^t
2,000 = 16,000 (1-0.35)^t
2,000 = 16,000 (0.65)^t
2,000/16,000 = 0.65^t
0.125 = 0.65^t
log(0.125) = log(0.65^t)
log(0.125) = log(0.65) t
log(0.125) / log(0.65) = t
4.82 = t

or 5 years

16,000 0.65 = 10,400
10,500 0.65 =   6,760
  6,760 0.65 =   4,394
  4,394 0.65 =   2,856.10
  2,856.1 0.65 = 1,856.47

Lanuel

Based on the calculations, the age of Devon's car is approximately equal to 5 years.

Given the following data:

Initial value = $16,000

Rate of depreciation = 35% = 0.35

Current value = $2,000

How to calculate the age of Devon's car?

Mathematically, the equation which can be used to determine the age of Devon's car is given by:

2,000 = 16,000(1 - r)^t

Where:

  • t is the age of the car in years.
  • r is the rate of depreciation.

Substituting the given parameters into the equation, we have:

2,000 = 16,000(1 - 0.35)^t

2,000 = 16,000(0.65)^t

2,000/16,000 = 0.65^t

0.125 = 0.65^t

Taking the log of both sides, we have:

log(0.125) = log(0.65^t)

log(0.125) = log(0.65) × t

t = log(0.125)/log(0.65)

t = 0.125/0.65

Age, t = 4.82 ≈ 5 years.

Read more on depreciation here: https://brainly.com/question/25806993

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