Question 435669
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^n - 1}}}
So, in general, we can write:
{{{S(n) = (2^n - 1)S(1)}}}
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(600,500,-5,25,-200000000,200000000,10*(2^x - 1))}}}