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Mr. Miller has a cupcake company. The amount of money earned is represented by
[tex]g(x) = 12\sqrt[3]{x+1}[/tex] 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, [tex]h(x)=12\sqrt[3]{x-2}+1[/tex]. What transformations have occurred from the original Cupcake company function, g(x)?

Respuesta :

semsee45

Answer:

a)  x = 26

b) (3 units right, 1 unit down)

Step-by-step explanation:

(a)

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

Divide both sides by 12:

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

Cube both sides:

[tex]\implies x+1 =3^3[/tex]

[tex]\implies x+1 =27[/tex]

Subtract 1 from both sides:

[tex]\implies x=26[/tex]

(b)

[tex]h(x)=g(x-3)+1[/tex]

translation of [tex]\left(\begin{array}{ccc}3\\1\end{array}\right)[/tex]

(3 units right, 1 unit down)

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