Question

Mrs. Galicia has a cupcake company. The amount of money earned is represented by g(x)=12∛x+1 where x is the number of years since 2015.


A. After how many years does she earn $36 ?

B. Mrs. Galicia changes the purchase price and the new function, hx=123x-2+1. What transformations have occurred from the original Cupcake company function, g(x)?


PLEASE SHOW ALL WORK!!!!!!!

Answer 1

Using the given function, it is found that:

a) She earns $36 after 26 years.

b) The original function was shifted 3 units to the right and 1 unit up.

What is the function?

Her profit in x years after 2015 is given by:

$g(x) = 12\sqrt[3]{x + 1}$

Item a:

She earns $36 after x years, considering that g(x) = 36, hence:

$g(x) = 12\sqrt[3]{x + 1}$

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

$\sqrt[3]{x + 1} = 3$

$(\sqrt[3]{x + 1})^3 = 3^3$

$x + 1 = 27$

$x = 26$

She earns $36 after 26 years.

Item b:

The new function is:

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

Which can be basically written as:

$h(x) = f(x - 3) + 1$

Hence the original function was shifted 3 units to the right and 1 unit up.

More can be learned about functions at https://brainly.com/question/25537936