Question

A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.262)e1.12567t bacteria per hour. how many bacteria will there be after three hours? (round your answer to the nearest integer.)

Answer 1

Answer:

5,274,027 bacteria

Step-by-step explanation:

First, we find the function of number of bacteria:

$N(t)=400(450.262)\,e^{1.12567t}\\ N(t)=180104.8\,e^{1.12567t}$

Now, we replace t=3 and operate.

$N(3) = 180104.8\,e^{1.12567(3)}=180104.8(29.2831)\\ N(3)=5274026.86888\approx 5274027$