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?

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.

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step-by-step explanation: