Question

Sandra bought a boat for $28,800. According to her insurance company the value of the boat depreciates 7% each year. What will the value of the boat be x years after she purchased it?

Answer 1

We have been given that Sandra bought a boat for $28,800. According to her insurance company the value of the boat depreciates 7% each year. We are asked to find the value of the boat x years after Sandra purchased it.

We will use exponential decay formula to solve our given problem.

An exponential decay function is in form
`y=a(1-r)^x`, where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 7% into decimal form.

`7\%=(7)/(100)=0.07`

Initial value of car is $28,800, so our function will be:

`y=$28,800(1-0.07)^x`

`y=$28,800(0.93)^x`

Therefore, the value of boat after x years would be
`y=$28,800(0.93)^x`.