Question

for your career project, you plan to design ans sell t-shirts. During the first 5 weeks of selling the shirts, the functions f(s)=4/3s-20 models your profit made, where s is the number of shirts sold. Your teacher mentions that by making a slight change to your printing procedure, you could double the profit per shirt sold. Find your new profit equation and describe how this change transforms the graph of f. Then determine the new profit you could make by selling 300 shirts

Answer 1

Using translation concepts, we have that:

• The new profit equation is f(x) = (8s/3) - 20, which is a vertical stretch by a factor of 2 of the graph of f(s).

• Selling 300 shirts, the new profit is of $780.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the profit function is given by:

f(s) = 4/3s - 20

To double the function, we multiply the slope by 2, hence the new profit equation is:

f(s) = 8/3s - 20.

This new function is a vertical stretch by a factor of 2 of the graph of f(s).

The new profit selling 300 shirts is given by:

f(300) = (8/3) x 300 - 20 = 8 x 100 - 20 = $780.

More can be learned about translation concepts at brainly.com/question/28373831

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