SOLUTION: The population P of a certain culture is expected to be given by a model p=100e^(rt) where r is a constant to be determined and t is a number of days since the original population
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Question 84942: The population P of a certain culture is expected to be given by a model p=100e^(rt) where r is a constant to be determined and t is a number of days since the original population of 100 was established. Find the value of r if the population is expected to reach 200 in 3 days. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The population P of a certain culture is expected to be given by a model p=100e^(rt) where r is a constant to be determined and t is a number of days since the original population of 100 was established. Find the value of r if the population is expected to reach 200 in 3 days.
:
100*e^(rt) = P
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Substitute for t and P
100*e^(3r) = 200
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Divide both sides by 100:
e^(3r) = 200/100
e^(3r) = 2
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Find the nat log of both sides:
ln(e^3r) = ln(2)
:
3r*ln(e) = ln(2); log equivalent of exponents
:
3r = .693147; remember the nat log of e is 1
:
r = .693147/3
:
r = .23105
:
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Check solution on a good calc: enter e^(3*.23105) = 2.0000
