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.
The profit, in x years after 2015, is given by:
[tex]p(x) = 12\sqrt[3]{x + 2}[/tex]
Item a:
She earns $36 after x years, considering x for which p(x) = 36, hence:
[tex]p(x) = 12\sqrt[3]{x + 2}[/tex]
[tex]36 = 12\sqrt[3]{x + 2}[/tex]
[tex]\sqrt[3]{x + 2} = 3[/tex]
[tex](\sqrt[3]{x + 2})^3 = 3^3[/tex]
[tex]x + 2 = 27[/tex]
[tex]x = 25[/tex]
She earns $36 after 25 years.
Item b:
The new function is:
[tex]h(x) = 12\sqrt[3]{x - 2} + 1[/tex]
At the domain, we have that [tex]x + 2 \rightarrow x - 2[/tex], that is, [tex]x \rightarrow x - 4[/tex], hence it was shifted right 4 units.
At the range, we have that [tex]h(x) = h(x - 4) + 1[/tex], hence it was shifted up 1 unit.
You can learn more about functions at https://brainly.com/question/24380382
