Question

A sailboat depreciates at 15% of its original value each year. If the sailboat was $9,500 at its time of purchase, what is the value of the sailboat after 7 years?

Answer 1

Answer: $ 3045.48

Explanation:

The exponential decay equation with rate of growth r in time period t is given by :-

`y=A(1-r)^t`, where A is the initial amount

Given : The rate of decay of population every year : 15% =0.15

The initial value = $9500

Then , the exponential growth equation in time period t is given by :-

`y=9500(1-0.15)^t=9500(0.85)^t`

After t= 7 years

The value of the sailboat will be :-

`y=9500(0.85)^(7)=3045.48233867\approx3045.48`

Hence, the value of the sailboat after 7 years= $3045.48.