Question

The following function represents the amount of money that Alisha has saved after w weeks:f(w)=20w+50A. What does the 20 represent in this situation?B. What does the 50 represent in this situation?C. How long would it take for Alisha to save $150?

Answer 1

The Solution:

Given that the function below represents the amount that Alisha saved after w weeks.

`f(w)=20w+50`

A.

The 20 represents the rate of change of Alisha's savings per week. That means it represents the amount by which Alisha's savings change from one week to another.

B.

The 50 represents the initial amount in Alisha's savings. That is, the amount in Alisha's saving at zero weeks.

C.

This means that we should find w when f(w)=$150

`\begin{gathered} f(w)=20w+50 \\ f(w)=150,\text{ Substituting we get} \\ 150=20w+50 \end{gathered}`

Collecting the like terms, we get

`\begin{gathered} 150-50=20w \\ 100=20w \\ \text{Dividing both sides by 20, we get} \\ (100)/(20)=(20w)/(20) \\ \\ 5=w \\ w=5\text{ w}eeks \end{gathered}`

Thus, it will take Alisha 5 weeks to save $150.