A new car is purchased for 16000 dollars. The value of the car depreciates at 13.75% per year. To the nearest tenth of a year, how long will it be until the value of the car is 2900 dollars

It will take 11.5 years

Step-by-step explanation:

In this question, we are concerned with calculating the amount of time it will take for the value of a new car to depreciate to a certain amount, given the price it was bought and the percentage of yearly depreciation.

To calculate this time, we need the appropriate exponential equation

Mathematically, that could be expressed as;

V = I (1-r) ^t

where V is the future car value which is $2,900

I is the initial car value which is $16,000

r is the rate of depreciation which is 13.75% which is same as 13.75/100 = 0.1375

and t is the time we want to calculate.

Thus, plugging the values, we have;

2900 = 16000 (1-0.1375) ^t

divide through by 16,000

0.18125 = 0.8625^t

Finding the log of both sides, we have

log 0.18125 = log0.8625^t

log 0.18125 = t log 0.8625

t = log 0.18125/log 0.8625

t = 11.546

To the nearest tenth of a year, t = 11.5 years