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Anna took a job that paid $100 the first week she qaa guaranteed a raise of 5% each week how much money will she make in all over 8 weeks round the answer to the nearest cent

Sagot :

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Answer:

140.71

Step-by-step explanation:

WEEK 1- 100

WEEK 2- 105

WEEK 3-110.25

WEEK 4-115.7625

WEEK 5-121.550625

WEEK 6-127.62815625

WEEK 7-134.009564063

WEEK 8-140.710042266

Facundo3141592idn

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

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