SOLUTION: Please help me to solve this problem. Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt . The count in the bacteria culture was 900 after 20 mi

Question 1056771: Please help me to solve this problem.
Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt
. The count in the bacteria culture was 900 after 20 minutes and 1600 after 30 minutes.
(a) What was the initial size of the culture?
(b) Find the population after 80 minutes.
(c) How many minutes after the start of the experiment will the population reach 10000?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me to solve this problem.
Assume that the number of bacteria follows an exponential growth model:
P(t)=Po*e^(kt)
. The count in the bacteria culture was 900 after 20 minutes and 1600 after 30 minutes.
900 = Po*e^(20k)
1600 = Po*e^(30k)
----------------------------
Divide to solve for "k"::
e^(10k) = 16/9
10k = ln(16/9) = 0.5754
k = 0.058
--------------
Equation:
P(t) = Po*e^(0.058t)
Solve for "Po"::

(a) What was the initial size of the culture?
900 = Po*e^(0.058*20)
900 = Po*3.19
Po = 282
-------------------------------
(b) Find the population after 80 minutes.
P(80) = 282*e^(0.058*80)
P(80) = 29,213
---------------------
(c) How many minutes after the start of the experiment will the population reach 10000?
Solve 10000 = 282*e^(0.058t)
----
e^(0.058t) = 35.46
0.058t = ln(35.46)
0.058t = 3.57
time = 61.52 minutes
------------
Cheers,
Stan H.
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