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 of
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Question 93511This question is from textbook Algebra and Trigonometry
: 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. This question is from textbook Algebra and Trigonometry
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.
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Substitute 200 for p, and 3 for t in the given equation:
100 * e^(3r) = 200
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e^(3r) = 200/100; divided both sides by 100
e^(3r) = 2
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ln(e^3r) = ln(2); find nat log of both sides
3r * ln(e) = ln(2); log equiv of exponents
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3r = .693147; Remember the nat log of e is 1
r = .693147/3
r = .231
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Check solution. using original population of 100 and r = .231
p = 100 * e^(3*.231)
p = 100 * e^.693
p = 100 * 1.9997; find e^.693 on a good calc
p = 199.97 ~ 200
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