A new car is purchased for 18500 dollars. The value of the car depreciates at 10.75%

per year. To the nearest year, how long will it be until the value of the car is 5000 dollars?

Answer: 11.5 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential decay function:

A = P (1 - r) ^ t

Where:

p = original value

r = depreciation rate (decimal form) = 10.75 / 100 = 0.1075

t = years

A = value after t years

Replacing with the values given:

5000 = 18500 (1 - 0.1075) ^t

Solving for t:

5000/18500 = (1 - 0.1075) ^t

0.27027027 = 0.8925 ^t

ln 0.27027027 = ln 0.8925 ^t

ln 0.27027027=t (ln 0.8925)

ln 0.27027027 / ln 0.8925 = t

11.5 years = t

Feel free to ask for more if needed or if you did not understand something.