Question

Mr. Miller has a cupcake company. The amount of money earned is represented by


`g(x) = 12\sqrt[3]{x+1}` where x is the number of years since 2015.
(a) After how many years does he earn $36
(b) Mr. Miller changes the purchase price and the new function,
`h(x)=12\sqrt[3]{x-2}+1`. What transformations have occurred from the original Cupcake company function, g(x)?

Answer 1

a) x = 26

b) (3 units right, 1 unit down)

Explanation:

(a)

`12\sqrt[3]{x+1} =36`

Divide both sides by 12:

`\implies \sqrt[3]{x+1} =3`

Cube both sides:

`\implies x+1 =3^3`

`\implies x+1 =27`

Subtract 1 from both sides:

`\implies x=26`

(b)

`h(x)=g(x-3)+1`

translation of
`\left(\begin{array}{ccc}3\\1\end{array}\right)`

(3 units right, 1 unit down)