A new car is purchased for 24900 dollars. The value of the car depreciates at 6.5% per year. To the nearest year, how long will it be until the value of the car is 14200 dollars?

Answer: it will take 8 years.

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P (1 - r) ^ t

Where

A represents the value of the after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

P = 24900 dollars

A = 14200 dollars

r = 6.5% = 6.5/100 = 0.065

Therefore

14200 = 24900 (1 - 0.065) ^t

14200/24900 = (0.935) ^t

0.5701 = (0.935) ^t

Taking log of both sides to base 10

Log 0.5701 = log0.935^t = tlog0.935

- 0.22 = t * - 0.0292

t = - 0.22 / - 0.0292

t = 8 years