Question

Mrs. Galicia has a cupcake company. The amount of money earned is represented by

Answer 1

Using the profit function, it is found that:

a) She earns $36 after 25 years.

b) The function was shifted right 4 units and up 1 units.

What is the profit function?

The profit, in x years after 2015, is given by:

$p(x) = 12\sqrt[3]{x + 2}$

Item a:

She earns $36 after x years, considering x for which p(x) = 36, hence:

$p(x) = 12\sqrt[3]{x + 2}$

$36 = 12\sqrt[3]{x + 2}$

$\sqrt[3]{x + 2} = 3$

$(\sqrt[3]{x + 2})^3 = 3^3$

$x + 2 = 27$

$x = 25$

She earns $36 after 25 years.

Item b:

The new function is:

$h(x) = 12\sqrt[3]{x - 2} + 1$

At the domain, we have that $x + 2 \rightarrow x - 2$, that is, $x \rightarrow x - 4$, hence it was shifted right 4 units.

At the range, we have that $h(x) = h(x - 4) + 1$, hence it was shifted up 1 unit.

You can learn more about functions at brainly.com/question/24380382