SOLUTION: Hi. "The population P of a certain culture is expected tp 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 pop

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Question 65737: Hi.
"The population P of a certain culture is expected tp 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. I need to find the value of r if the population is expected to reach 200 in 3 days."
Answer by funmath(2873) About Me  (Show Source):
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"The population P of a certain culture is expected tp 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. I need to find the value of r if the population is expected to reach 200 in 3 days."
P=200
t=3
200=100e%5E%28r%2A3%29
200%2F100=100e%5E%283r%29%2F100
2=e%5E%283r%29 Take the natural log of both sides
ln%282%29=ln%28e%5E%283r%29%29 remember: ln(a^m)=mln(a)
ln%282%29=3rln%28e%29
ln%282%29=3r%281%29 remember: ln(e)=1
ln%282%29=3r
ln%282%29%2F3=3r%2F3
r=ln%282%29%2F3
r=.6931471806%2F3
r=.2310490602 Round off to whatever you are asked for.
Happy Calculating!!!