Question

A car had a value of $10,000 and depreciates at a rate of 7% a year. What is the cars value after 3 years.​

Answer 1

Explanation:

The exponential decay function is

`v(t)=a(b)^t` where a is the initial value of the car, b is the rate of decay, and t is the time in years. Our rate of decay can also be written as (1 - r) where r is the depreciation in decimal form. Our equation looks like this:

`v(t)=10000(1-.07)^t` which simplifies to

`v(t)=10000(.93)^t` Now we can solve our problem for any number of years you'd like. We've been tasked to find the value of the car after 3 years, so:

`v(t)=10000(.93)^3` which simplifies a bit to:

`v(t)=10000(.804357)` so

v(t) = 8043.57