SOLUTION: Jasmine has accepted a new job with an interesting pay scale. She will earn $ 10 for the first month, $ 20 for the second month, $ 40 for the third month, and so on. Each month he

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: Jasmine has accepted a new job with an interesting pay scale. She will earn $ 10 for the first month, $ 20 for the second month, $ 40 for the third month, and so on. Each month he      Log On


   

Question 435669: Jasmine has accepted a new job with an interesting pay scale. She will earn $ 10 for the first month, $ 20 for the second month, $ 40 for the third month, and so on. Each month her salary will be twice that of the previous month. Develop a formula that will give Jasmine's total income through n months. How much will she have received after 2 years, giving your answer in standard form correct to two significant figures?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
We need to find the accumulated salary through n months.
Let's look at the first few months.
Let S(n) = the total salary through the n-th month
We can write:
S(1) = 10
S(2) = 10 + 20 = 30
S(3) = 30 + 40 = 70
S(4) = 70 + 80 = 150
Now we try to find an expression for S(n) in terms of S(1):
S(2) = S(1) + 20 = S(1) + 2S(1) = 3S(1)
S(3) = S(2) + 40 = S(2) + 4S(1) = S(1) + 2S(1) + 4S(1) = 7S(1)
For a given n, the multiplier can then be expressed as 2%5En+-+1
So, in general, we can write:
S%28n%29+=+%282%5En+-+1%29S%281%29
Let's check our formula for n=4
S(4) = (2^4 - 1)S(1) = 15S(1) = 150
After 2 years, the total salary will be:
S(24) = (2^24 - 1)S(1) = $167,772,150 (not sure about the "standard form")
The graph below shows the rate at which the cumulative salary grows:
graph%28600%2C500%2C-5%2C25%2C-200000000%2C200000000%2C10%2A%282%5Ex+-+1%29%29