Calculating exponential revenue growth

[super_steph]

A company is making $50,000 in revenue each month. During the next 12 months, the company wants to make 1.5M in revenue within that time frame. What % growth is needed each month if the first month's revenue is $50,000 and each month makes more in revenue than the previous month?

I know how to calculate exponential growth from 0 to $1.5M and I know how to calculate it if starting from another base value besides 0. But I can't figure out how to calculate it if I specifically want month one's revenue to be a specific value.

Your help is much appreciated!

 

[HallsofIvy]

Let "r" be the rate of growth. Then the revenue for 12 months is 50000+ (1+ r)500000+ (1+ 2r)50000+ ... + (1+ 11r)50000= 12(50000)+ 50000r(1+ 2+ 3+ ...+ 9+ 10+ 11).

To see what that sum, S= 1+ 2+3+...+ 9+ 10+ 11, notice that S= 11+ 10+ 9+ ...+ 3+ 2+ 1 and add:
S= 1+ 2+ 3+...+ 9+ 10+ 11
S= 11+ 10+ 9+ ...+ 3+ 2+ 1

Adding "vertically" each adds to 12 and there are 11 so 2S= 11(12), S= 11(6)= 66.

So you have 12(50000)+ 50000r(66)= 600000+ 3300000 r= 1500000.

Solve that for r.