Question

A student sells ice cream bars. Her weekly salary is given by S(x) = 0.60x + 300, where x is the number of ice cream bars sold. Her employer determines the amountwithheld for taxes using the function W(x) = 0.10x, where x is her weekly salary. Write the amount withheld as a function of the number of ice cream bars sold. Hint: Usecomposition.The amount withheld as a function of the number of ice cream bars sold is W(x) =(Simplify your answer. Use integers or decimals for any numbers in the expression.)

Answer 1

To find the amount withheld as a function of the number of ice cream bars sold, we must compose the 2 given functions in the problem

The 2 funtions are:

$\begin{gathered} S(x)=0.6x+300 \\ W(x)=0.1x \end{gathered}$

As we want to find the amount withheld as a function of the number of ice cream bars sold, we need to compose S(x) into W(x).

Mathematically it is represented as:

$W(x)\circ S(x)$

Then, we need to calculate the composition

$\begin{gathered} W(x)\circ S(x)=W(S(x)) \\ \Rightarrow W(0.6X+300)=0.1(0.6x+300)=0.06x+30 \end{gathered}$

So, the amount withheld as a function of the number of ice cream bars sold is

$W(x)=0.06x+30$

Where x is the number of ice cream bars sold