Question

the number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)5t. There are 25 bacteria present initially and a biologist wishes to find out how many hours will elapse until there are 4,000 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 4,000 = 25(10)5t?

Answer 1

`4000 = 25(10)^(5t) \\ 160 = (10)^(5t) \\ 5t = (log(160))/(log(10)) \\ 5t = log(160) \\ 5t = 2.204 \\ t = 0.441`
Therefore in 0.441 hours, the 25 bacteria will have multiplied to reach 4,000.