Question

A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.263)e1.12567t bacteria per hour. How many bacteria will there be after three hours?

Answer 1

Answer:

11,713 bacteria

Step-by-step explanation:

Integrating the growth rate function gives us the population of bacteria at any given moment 't', in hours:

$r(t) = (450.263)e^{1.12567t} \\\int\ {r(t)} \, dt =P(t) = \frac{450.263}{1.12567}*e^{1.12567t} +C$

Since at t=0, P(t) = 400, the value of C is:

$P(0) = \frac{450.263}{1.12567}*e^{1.12567*0} +C\\400 = 400*1+C\\C=0$

The number of bacteria after 3 hours is:

$P(3) = 400*e^{1.12567*3}\\P(3) =11,713$