By using an exponential equation, we will see that in the first 8 weeks she makes $954.90.
How much will she make in 8 weeks?
We know that the first week she makes $100, and for each week after that, she makes an extra 5%.
Then, the second week she makes:
W(2) = $100*(1 + 5%/100%) = $100*(1.05)
The third week she makes:
W(3) = $100*(1.05)*(1 + 5%/100%) = $100*(1.05)^2
We already can see the exponential pattern, for the N-th week, the salary will be:
W(N) = $100*(1.05)^(N - 1)
Then what she wins in the first 8 weeks is:
- W(1) = $100
- W(2) = $100*1.05 = $105
- W(3) = $100*(1.05)^2 = $110.25
- W(4) = $100*(1.05)^3 = $115.75
- W(5) = $100*(1.05)^4 = $121.55
- W(6) = $100*(1.05)^5 = $127.63
- W(7) = $100*(1.05)^6 = $134.01
- W(8) = $100*(1.05)^7 = $140.71
Now we just need to add these 8 values, we will see that the total money that she makes in these 8 weeks is:
M = $954.90
If you want to learn more about exponentials, you can read:
https://brainly.com/question/11464095
