This depreciation problem indicates that we are using an exponential decay model
ID: 2859161 • Letter: T
Question
This depreciation problem indicates that we are using an exponential decay model,
Q(t) = Q0ekt
where t is nonnegative, Q0 is the (positive) amount of the quantity present initially, and k is a positive constant.
Let t be the number of years since the purchase of the machinery. Therefore, t = 0 was the time when the machinery was purchased.
We must first find the decay constant k using the information provided about the initial value and the value 5years later.
The initial quantity in this case is the purchase price or initial value of the machinery. Since the initial purchase price was $500,000 we have
We are told that the machinery was purchased 5 years ago, therefore at the time when the machinery is valued at $370,000 we know that t = 5. Therefore we have
Explanation / Answer
given Q(t) = Q0ekt
initial purchase price was $500,000 we have
Q0 =500000
Q(5) =370000
370000 = 500000ek*5
ek*5=(370000/500000)
e5k=37/50
-5k=ln(37/50)
-5k=ln(37/50)
-5k=-0.3011
k=0.06
Therefore we have k=0.06