Question

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 represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon's car? Use a calculator and round your answer to the nearest whole number.

Answer 1

Given :

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%.

Its current value is $2,000.

To Find :

Age of car.

Solution :

Price of car after 1 year :

$P_1=P_o(1-0.35)$

Price of car after 2 year :

$P_2=P_1(1-0.35)\\\\P_2=[P_o(1-0.35)](1-0.35)\\\\P_2=P_o(1-0.35)^2$

So, price of car after n years.

$P_n=P_o(1-0.35)^n$

$2000=16000(1-0.35)^n\\\\0.65^n=0.125\\\\n\times log(0.56)=log(0.125)\\\\n=\dfrac{log(0.125)}{log(0.56)}\\\\n=3.58$

Therefore, age of car in nearest whole number is 4 years.

Hence, this is the required solution.