We will have the points (0, 50) & (2, 100), using this we can find a linear equation that models the money over time. We first find the slope:
[tex]m=\frac{100-50}{2-0}\Rightarrow m=25[/tex]
Now, using one of the points we replace in:
[tex]y-y_1=m(x-x_1)[/tex]
We will use (0, 50), but we could use any other point of the line. Now, we replace:
[tex]y-50=25(x-0)[/tex]
And now, we solve for y:
[tex]\Rightarrow y=25x+50[/tex]
Now, in order to get the saving for each month, we replace x by 5, 10, 15 & 20 respectively:
*5 weeks:
[tex]y=25(5)+50\Rightarrow y=175[/tex]
*10 weeks:
[tex]y=25(10)+50\Rightarrow y=300[/tex]
*15 weeks:
[tex]y=25(15)+50\Rightarrow y=425[/tex]
*20 weeks:
[tex]y=25(20)+50\Rightarrow y=550[/tex]
From this, we have that the savings for 5, 10, 15 & 20 weeks are 175, 300, 425 & 550 respectively.
