Question

The value of a new car bought for $20,000 decreased by 10% per year. How do you write an exponential decay model for the value of the car and use the model to estimate the value after one year?

Answer 1

`f(x)=20000(.9)^x`

Explanation:

Let `M=20,000` then we decrease by `10%` annually so lets consider that we retain `90%` value annually then we know that for year 1 its `f(1) = M(.9)` and for the next year we have
`f(2) = M(.9)(.9) = M(.9)^2`

So this pattern repeats and for any `x` future values