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 [tex]y=a(1-r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Decay rate in decimal form,
x = Time.
Let us convert 7% into decimal form.
[tex]7\%=\frac{7}{100}=0.07[/tex]
Initial value of car is $28,800, so our function will be:
[tex]y=$28,800(1-0.07)^x[/tex]
[tex]y=$28,800(0.93)^x[/tex]
Therefore, the value of boat after x years would be [tex]y=$28,800(0.93)^x[/tex].
