if a bacteria population triples every three hours, how long will it take a population of 20 colonies to grow to 1,000?

Question

anonymous · Answer

I'm going over practice problems during break and I am stumped on this one. Forgot how to do exponential...The answer in my book says 10.683 hours.

anonymous · Answer

Thank god its practice, il still try to figure it out

anonymous · Answer

yeah i know! but out of everything I am reviewing I am totally missing something here...I'm pretty sure I need to find the rate and then just plug that into the log.

anonymous · Answer

yeah

anonymous · Answer

Are you familiar with the exponential growth equation $$N = N _{0} e ^{kt}$$

anonymous · Answer

yes

anonymous · Answer

Well, we know N0 is the initial population.  N0 = 20.  This corresponds to time t = 0.

We also know that the population, N, triples every three hours.  Thus when t = 3, N = 60.  Plug these numbers in and solve for k.  Then you will have a general equation.

anonymous · Answer

awwwwwwww, yes! thank you. i have been refreshed.