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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)?

User Ashutosh A
by
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1 Answer

7 votes

Answer:

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)

User Rohit Sangal
by
3.6k points