Question 921034
Assume that the number of bacteria follows an exponential growth model:
 {{{P(t)=Po*e^(kt)}}} where:
P(t) = resulting amt after t time
Po -= initial amt
t = growth period
k = growth constant
:
 The count in the bacteria culture was 900 after 10 minutes and 1000 after 35 minutes.
Find k, went from 900 to 1000 in 25 min
{{{900*e^(25k) = 1000}}}
{{{e^(25k) = 1000/900}}}
{{{e^(25k) = 10/9}}}
using natural logs
{{{25k = ln(10/9)}}}
25k = .10536
k = {{{.10536/25}}}
k = .0042 
 
(a) What was the initial size of the culture?
{{{Po*e^((.0042*35)) = 1000}}}
Po = {{{1000/(e^((.0042*35)))}}}
Po = 863.3 initial size of the culture
:
(b) Find the population after 70 minutes.
P(t) = {{{863*e^((.0042*70))}}}
P(t) = 1158 after 70 min
:
(c) How many minutes after the start of the experiment will the population reach 11000? 
{{{863*e^((.0042t)) = 11000}}}
{{{e^((.0042t)) = 11000/863}}}
using nat logs
{{{.0042t = ln(11000/863)}}}
.0042t = 2.54523
t = {{{2.54523/.0042}}}
t = 606 minutes to increase to 11000