Question

19. For your career project, you plan to design and sell T-shirts. During the first
5 weeks of selling the shirts, the function 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
number of shirts you could sell. Find your new profit equation and describe
how this change transforms the graph off. Then determine the new profit
you could make by selling 300 shirts

Answer 1

Using translation concepts, we have that:

• The new equation is f(s) = (8/3)s - 20.

• The effect on the graph is that it is a vertical stretch by a factor of 2 of the function f(s).

• Selling 300 shirts with the new function, you obtain a profit 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.

The profit function given in the problem is:

f(s) = (4/3)s - 20.

From this function, we get that the profit with a single shirt sold is of $4/3. To double the profit, this amount has to be multiplied by 2, hence the new function is:

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

Which is a vertical stretch by a factor of 2 of the graph of f(s).

When 300 shirts are sold, the profit is then given by:

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

More can be learned about translation concepts at https://brainly.com/question/4521517

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