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15 votes
Delta has decided to start a side business as a photographer. She purchases a camera for $1600 but it loses value at 12.5% per year. How much will her camera be worth after 5 years? Round to the nearest cent.

User Roel
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1 Answer

23 votes
23 votes

Given:

Initial value of camera = $1600

Percentage decrease = 12.5% per year = 0.125

Time, t = 5 years

Let's find the value of the camera after the given time (5 years).

To find the value of the camera, apply the exponential decay formula:


A=P(1-r)^t

Where:

A is the final value

P is the initial value = $1600

r is the rate of change = 0.125

t is the time = 5 years

Thus, we have:


\begin{gathered} A=1600(1-0.125)^5 \\ \\ A=1600(0.875)^5 \\ \\ A=1600(0.5129) \\ \\ A=820.65 \end{gathered}

Therefore, the value of the camera after 5 years will be $820.65

ANSWER:

$820.65

User TomL
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2.8k points