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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?

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

Answer:

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

Step-by-step explanation:

Formula for exponential decay:   [tex]A=P(1-r)^t[/tex], where [tex]P=[/tex] Initial value, [tex]A=[/tex] Final value, [tex]r=[/tex] Decay rate in decimal form and [tex]t=[/tex] 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,  [tex]P=9500,\ \ r=15\%=\frac{15}{100}=0.15,\ \ t=7\ years[/tex]

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

[tex]A=9500(1-0.15)^7\\ \\ A=9500(0.85)^7\\ \\ A=3045.4823...[/tex]

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

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