devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. its current…

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 2,000 = 16,000(1 - r)^t represents the situation, where t is the age of the car in years and r is the rate of depreciation. about how old is devons car? use a calculator and round your answer to the nearest whole number.\no 1 year\no 2 years\no 5 years\no 8 years

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 2,000 = 16,000(1 - r)^t represents the situation, where t is the age of the car in years and r is the rate of depreciation. about how old is devons car? use a calculator and round your answer to the nearest whole number.\no 1 year\no 2 years\no 5 years\no 8 years

Answer

Answer:

C. 5 years

Explanation:

Step1: Identify values

$2000 = 16000(1 - 0.35)^t$

Step2: Simplify the equation

$\frac{2000}{16000}=(0.65)^t$, so $0.125=(0.65)^t$.

Step3: Take the natural - log of both sides

$\ln(0.125)=t\ln(0.65)$.

Step4: Solve for t

$t=\frac{\ln(0.125)}{\ln(0.65)}\approx\frac{- 2.079442}{- 0.430783}\approx4.83\approx5$.