Andreas buys a new sailboat for $15,540. He estimates that

Vikolers6 2021-12-26 Answered
Andreas buys a new sailboat for $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?
F. y=15,540(1.05)x
G. y=15,540(0.95)x
H. y=15,540(0.95)x
J. y=15,540(1.05)x
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Expert Answer

Natalie Yamamoto
Answered 2021-12-27 Author has 22 answers
The exponential decay model is given by,
y=a(1r)t where,
a is the initial amount
r is the decay rate
t is the time period
(1r) is the decay factor
From the given data the following equation is formulated.
y=15,540(10.05)x
y=15,540(0.95)x
Therefore, the correct option is G.
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Mary Herrera
Answered 2021-12-28 Author has 37 answers
We have to use a straight-line depreciation model here as the asset depreciates by the same amount each year. The model is given below.
y=p(1r)x
In the model, p is the purchase value of the asset, r is the yearly rate of depreciation, and x is the number of years that the asset has been held for.
Using the information in the question, p=$15540 and r=0.05.
So, the model is:
y=15540(10.05)x=15540(0.95)x
So, the correct option is b.
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user_27qwe
Answered 2022-01-05 Author has 229 answers

Given, initial price of sailboat, P0=$15,540
Price of the sailboat depreciate by 5% each year.
Thus, price of sailboat after 1 year =P00.05P0=0.95P0
Similarly, price of sailboat after 2 years =0.95P00.05(0.95P0)
=0.95P0(10.05)
=(0.95)2P0
Therefore, price of sailboat after x years =(0.95)xP0
=15,540(0.95)x
Answer: The exponential model for the price of boat (y) after x years is
y=15,540(0.95)x

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