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

The value of the sailboat after 7 years is $3045.4823...

Explanation:

Formula for exponential decay:
`A=P(1-r)^t`, where
`P=` Initial value,
`A=` Final value,
`r=` Decay rate in decimal form and
`t=` Time duration.

The sailboat was $9,500 at its time of purchase and it depreciates at 15% of its original value each year.

So here,
`P=9500,\ \ r=15\%=(15)/(100)=0.15,\ \ t=7\ years`

Plugging these values into the above formula......

`A=9500(1-0.15)^7\\ \\ A=9500(0.85)^7\\ \\ A=3045.4823...`

So, the value of the sailboat after 7 years is $3045.4823...

Answer 2

Its value is multiplied by (1 -15%) = 0.85 each year.
.. $9500*0.85⁷ ≈ $3045 . . . . . value after 7 years