Question 1056771
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)
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Divide to solve for "k"::
e^(10k) = 16/9
10k = ln(16/9) = 0.5754
k = 0.058
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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
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(b) Find the population after 80 minutes.
P(80) = 282*e^(0.058*80)
P(80) = 29,213
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(c) How many minutes after the start of the experiment will the population reach 10000? 
Solve 10000 = 282*e^(0.058t)
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e^(0.058t) = 35.46
0.058t = ln(35.46)
0.058t = 3.57
time = 61.52 minutes
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Cheers,
Stan H.
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