precalc question

Question

A population of fruit flies grows exponentially. At the beginning of the experiment, the population size is 400. After 21 hours, the population size is 546.  

a) Find the doubling time for this population of fruit flies. (Round your answer to the nearest tenth of an hour.)

   hours.

b) After how many hours will the population size reach 890? (Round your answer to the nearest tenth of an hour.)

   hours

Answer 1

546/400= e^21t

ln(546/400) = 21t

t = ln(1.365)/21 = about .01482

A = Pe^.01482t

doubling time is when

2 = e^.01482t

ln2 = .01482t

t = ln2/.01482 = 46.78 hours = doubling time

= about 46.8 hours

890 = 400e^.01482t

890/400 = e^.01482t

ln(89/40) = .01482t

t = ln(89/40)/.01482 = 53.96 hours

= about 54.0 hours