MODELING REAL LIFE Recently, bookstore sales have been declining. The sales (in billions of dollars) can be modeled by the function f(t) = -1/4t+ 11.3, where t is the number of years since 2016. Transform the graph off to model sales that decrease at twice this rate. Explain how this affects bookstore sales in 2024.

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23-08-2022
Mathematics

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MODELING REAL LIFE Recently, bookstore sales have been declining. The sales (in billions of dollars) can be modeled by the function f(t) = -1/4t+ 11.3, where t is the number of years since 2016. Transform the graph off to model sales that decrease at twice this rate. Explain how this affects bookstore sales in 2024.

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joaobezerra joaobezerra · Answer 1 · 2022-08-30T18:10:50+02:00

The linear function that in which the sales would decrease twice as fast is:

f(t) = -1/2t + 11.3.

The change means that the sales would be 2 billion less in 2024.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, the function is:

f(t) = -1/4t + 11.3.

The function is decreasing, as it has a negative slope. To decrease twice as fast, the slope has to be multiplied by 2, hence the function would be:

f(t) = -1/2t + 11.3.

2024 is 8 years after 2016, hence, for both cases:

f(t) = -1/4(8) + 11.3 = 9.3 billion sales.

f(t) = -1/2(8) + 11.3 = 7.3 billion sales.

The change means that the sales would be 2 billion less in 2024.

More can be learned about linear functions at https://brainly.com/question/24808124

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