Given:
Initial amount = 8
To find next week's amount, we multiply this week's amount by 4.
To find:
A formula that gives the amount A after T weeks.
Solution:
We have,
Initial amount = 8
According to the question,
Amount of next week = 4 × Amount of this week
Amount after one week is
[tex]A=4\times 8[/tex]
Amount after two week is
[tex]A=4\times (4\times 8)[/tex]
[tex]A=4^2\times 8[/tex]
Amount after T week is
[tex]A=4^T\times 8[/tex]
[tex]A=8(4)^T[/tex]
Therefore, the required formula that gives the amount A after T weeks is [tex]A=8(4)^T[/tex].
