Question

On Day 16, Ebony deposited $100 into her account. On each day after Day 16, segment 5, Ebony made adeposit, and those deposits were equal to each other.(a) Explain how you can determine, just by looking at the graph, whether the amounts she depositedafter Day 16 were each less than $100, $100, or more than $100.(b) Use the graph to estimate B(21) in hundreds. Explain how you determined this estimate. Then showhow you can estimate the amount of money Ebony deposited into her account each day after Day 16.

Answer 1

Given that on day 15 the balance was $0 and on day 16 the balance is $100, then we have:

`\begin{gathered} \text{slope:} \\ m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(100-0)/(16-15)=100 \\ \text{for point (15,0) and slope m=100:} \\ y-y_0=m(x-x_0) \\ \Rightarrow y-0=100(x-15) \\ \Rightarrow y=100x-1500 \end{gathered}`

we have that the relation function for this period is B(x)=100x-1500. Then for x=21 we have the following:

`\begin{gathered} B(x)=100x-1500 \\ B(21)=100\cdot21-1500=2100-1500=600 \\ \end{gathered}`

therefore, using the relation function, we have that B(21) = 600.

To find the amount of money deposited into the account after day 16, we have to find B(17), B(18), B(19) and B(20):

`\begin{gathered} B(17)=100\cdot17-1500=1700-1200=200 \\ B(18)=100\cdot18-1500=1800-1500=300 \\ B(19)=100\cdot19-1500=1900-1500=400 \\ B(20)=100\cdot20-1500=2000-1500=500 \end{gathered}`