Answer:
It will take 11.5 years
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