Jane & Joe own a graphic design store. They recently purchased a new commercial

Question

Jane & Joe own a graphic design store. They recently purchased a new commercial printer which cost $9,000. Due to depreciation they already have a plan to sell the printer in 5 years for $6,000 and replace it. Assuming that the value of this printer depreciates in an exponential fashion according to the model ?? = ??????????, where ???? represents the initial value of the printer and r represents the annual depreciation rate, find the exact exponential equation that models the value of this printer over time.

Explanation / Answer

Use:
A = P*e^(r*t)
where,
A: final amount
P: Present Value
r: rate componded continuously in decimal
t: time in years

A = P*e^(r*t)
6000.0 = 9000.0*e^(r*5.0)
0.6667 = e^(r*5.0)
r*5.0 = ln(0.6667)
r*5.0 = -0.4055
r = -8.109*10^-2
which -8.11 %
Answer:   rate of depreciation = -8.11 %
Actual equation is:
A = 9000 * e^(-8.11*t)

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