Question 1005660
 Bacteria were introduced to a petri dish.
 Two hours after the introduction, there were 120411 bacteria.
 After seven hours since the introduction, there were 1083699 bacteria.
:
1.) Find the growth rate of the bacteria. (round to 3 decimal places)
Write an equation for each scenario
P*e^(2r) = 120411
P = {{{120411/(e^(2r))}}}
and
P*e^(7r) = 1083699
P = {{{1083699/(e^(7r))}}}
replace P from the 1st equation
{{{120411/(e^(2r))}}}*e^(7r) = 1083699
Cancel the e^(2r)
120411*e^(5r) = 1083699
e^(5r) = {{{1083699/120411}}} 
Find the ln of both sides (ln(e)= 1)
5r = 2.197
r = .439 is the growth rate
:
2.) How many bacteria were initially introduced to the Petri dish? (Round to the nearest bacteria).
P = initial amt
P * e^(2*.439) = 120411
P * 2.40698 = 120411
P = {{{120411/2.40698}}}
P = 50046 bacteria initially
:
3.) How many bacteria will there be after 12 hours? (Round to the nearest bacteria).
A = 50046*e^(12*.439)
A = 9,710,301 bacteria after 12 hrs
:
4.) How long does it take for the bacteria colony to reach 361233 bacteria? (round to 2 decimal places)
50046*e^(.439t) = 361233
e^(.439t) = {{{361233/50046}}}
find the ln of both sides
.439t = 1.9766
t = {{{1.9766/.439}}}
t = 4.50 hrs