Aculture started with 3000 bacteria. after 6 hours, it grew 3600 bacteria. predict how many bacteria will be present after 13 hours

Hi! in this cases, we usually use a exponential model to describe the growth of the culture.

f(t) = 3000*exp(k*t) where k is a constant.

is easy to see that in t = 0, f(0) = 3000 which is the number at the start.

after 6 hours, we have 3600 bacteria, so:

f(6) = 3000*exp(k*6) = 3600

exp(k*6) = 3600/3000

k = ln(3600/3000)/6 = 0.03

So our exponential is f(t) = 3000*exp(0.03*t)

after 13 hours we get f(13) = 3000*exp(0.03*13) = 4431 total bacteria.

the answer is ! ?