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* log(0.56)=log(0.125)\\\\n=(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.