SOLUTION: 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.)

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)
2.) How many bacteria were initially introduced to the Petri dish? (Round to the nearest bacteria).
3.) How many bacteria will there be after 12 hours? (Round to the nearest bacteria).
4.) How long does it take for the bacteria colony to reach 361233 bacteria? (round to 2 decimal places)
Use Pe^rt equation!
PLEASE HELP ME ! I really have to understand this !
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
and
P*e^(7r) = 1083699
P =
replace P from the 1st equation
*e^(7r) = 1083699
Cancel the e^(2r)
120411*e^(5r) = 1083699
e^(5r) =
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 =
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) =
find the ln of both sides
.439t = 1.9766
t =
t = 4.50 hrs

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