Question

Janice receives $.40 per pound for 1 to 99 pounds of aluminum cans he recycles. he receives $.50 per pound if you are cycles more than 100 pounds. is the amount of money Janice receives a function of the weight of the cans here cycles? Explain your reasoning.

Answer 1

`M=\left\{\begin{matrix}0.4x &x\leq99 \\ 0.5x &x>100 \\ \end{matrix}\right.`

Explanation:

Function modeling

Real-life situations often require the help of mathematics to model numerically what happens when the variables involved can change. It could even be used to predict some expected outcomes from those models.

The problem states Janice receives $.40 per pound when he recycles less or equal than 99 pounds of aluminum. If x is the number of recycled pounds, then the amount of money he receives is

`M=0.4x`

We also know that if he recycles more than 100 pounds of aluminum, the pay increases to $0.5 per pound. In that case, the amount of money is

`M=0.5x`

This is a case where the function is defined differently depending on the conditions of the input variable x. It's called a piecewise function. The function can be written as

`M=\left\{\begin{matrix}0.4x &x\leq99 \\ 0.5x &x>100 \\ \end{matrix}\right.`

Note the function is not well constructed because there is a gap for x=100 where M is not defined. If we establish that for 100 pounds the payment is $0.5, then the second piece would include x=100