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

F.

G.

H.

J.

Natalie Yamamoto

Beginner2021-12-27Added 22 answers

The exponential decay model is given by,

$y=a{(1-r)}^{t}$ where,

a is the initial amount

r is the decay rate

t is the time period

$(1-r)$ is the decay factor

From the given data the following equation is formulated.

$y=15,540{(1-0.05)}^{x}$

$y=15,540{\left(0.95\right)}^{x}$

Therefore, the correct option is G.

a is the initial amount

r is the decay rate

t is the time period

From the given data the following equation is formulated.

Therefore, the correct option is G.

Mary Herrera

Beginner2021-12-28Added 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.

$y=p{(1-r)}^{x}$

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,$p=\mathrm{\$}15540\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}r=0.05}$ .

So, the model is:

$y=15540{(1-0.05)}^{x}=15540{\left(0.95\right)}^{x}$

So, the correct option is b.

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:

So, the correct option is b.

user_27qwe

Skilled2022-01-05Added 375 answers

Given, initial price of sailboat,

Price of the sailboat depreciate by 5% each year.

Thus, price of sailboat after 1 year

Similarly, price of sailboat after 2 years

Therefore, price of sailboat after x years

Answer: The exponential model for the price of boat (y) after x years is

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