# calculus

posted by
**Jake**
.

a bacteria pop. grows exponentially. There are 1500 bacteria after 3 hours and 20,000 after 8 hours.

ahving trouble finding the initial bacteria pop.

thanks for the help

In five hours the population get's larger by a factor 13 + 1/3----->

N(t) = N_0 * (13 + 1/3)^(t/5 hours)

Insert in here t = 3 hours and solve for N _0:

N_0 = N(3 hours)* (13 + 1/3)^(-3/5) = 317

thanks