I need a clearer understanding of how to solve: John decides to build a program capable of identifying cancer cells.  He gets initial funding of $100,000 for the first 5 months of research.  His research ends up taking 10 times that long and every month after those first 5 took 50% more funding per month.  How much did his research cost?
The research ended up taking 5*10=50 months
So he paid for expensive research for 50-5=45 months
Each month of research at the cheaper stage cost 100,000/5=$20,000
So the more expensive research cost 20,000*1.5=$30,000
So that research cost 45*30,000=$1,350,000
So the total cost was 1,350,000+100,000=$1,450,000