Vikolers6

2021-12-26

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. $y=15,540{\left(1.05\right)}^{x}$
G. $y=15,540{\left(0.95\right)}^{x}$
H. $y=-15,540{\left(0.95\right)}^{x}$
J. $y=-15,540{\left(1.05\right)}^{x}$

Natalie Yamamoto

The exponential decay model is given by,
$y=a{\left(1-r\right)}^{t}$ where,
a is the initial amount
r is the decay rate
t is the time period
$\left(1-r\right)$ is the decay factor
From the given data the following equation is formulated.
$y=15,540{\left(1-0.05\right)}^{x}$
$y=15,540{\left(0.95\right)}^{x}$
Therefore, the correct option is G.

Mary Herrera

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.
$y=p{\left(1-r\right)}^{x}$
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, .
So, the model is:
$y=15540{\left(1-0.05\right)}^{x}=15540{\left(0.95\right)}^{x}$
So, the correct option is b.

user_27qwe

Given, initial price of sailboat, ${P}_{0}=15,540$
Price of the sailboat depreciate by 5% each year.
Thus, price of sailboat after 1 year $={P}_{0}-0.05{P}_{0}=0.95{P}_{0}$
Similarly, price of sailboat after 2 years $=0.95{P}_{0}-0.05\left(0.95{P}_{0}\right)$
$=0.95{P}_{0}\left(1-0.05\right)$
$=\left(0.95{\right)}^{2}{P}_{0}$
Therefore, price of sailboat after x years $=\left(0.95{\right)}^{x}{P}_{0}$
$=15,540\left(0.95{\right)}^{x}$
Answer: The exponential model for the price of boat (y) after x years is
$y=15,540\left(0.95{\right)}^{x}$

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