SOLUTION: The count in a bacteria culture was 600 after 10 minutes and 2000 after 35 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Fi

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Question 1159189: The count in a bacteria culture was 600 after 10 minutes and 2000 after 35 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?

Find the doubling period.

Find the population after 120 minutes.

When will the population reach 10000
Answer by ankor@dixie-net.com(22740) (Show Source):
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The count in a bacteria culture was 600 after 10 minutes and 2000 after 35 minutes.
Assuming the count grows exponentially,
Using the form that a*b^x = y
x=10, y=600

x=35, y=2000

replace a with

cancel b^10

ln(b) = ln(3.333)/25}}}
ln(b) = .048159
b = 1.049337
Find a
a =
a =
a = 370.7
The equation

:
What was the initial size of the culture?
x=0, therefore 370.7 is the initial amt
:
Find the doubling period.

x*ln(1.049337) = ln(2)

x = 14.4 min
:
Find the population after 120 minutes.

y = 370.7*323.443
y = 119,900.5
:
When will the population reach 10000

x*ln(1.049337) = ln(26.976)

x = 68.42 min
:
looks like this