math word problem

Question

Suppose that the number of bugs in a rain-forest is growing exponentially.  If there were 2880 bugs after 3 weeks and 5120 bugs after 5 weeks, how many bugs were there initially? 

Answer 1

2880 in 3 weeks

5120 in 5 weeks

how many originally in 0 weeks??

2880=Poe^3r

5120=Poe^5r

2 equations 2 unknowns, solve for Po=original amount

divide last by 2nd to last equation to get

512/288 = 103/72 = e^5r/e^3r= e^2r

e^2r = 103/72

2r = ln(103/72)

r = .5ln(103/72)

2880 = Po(e^3(103/72)

Po= 2880/e^(103/24) = about 478.38= original amount