SOLUTION: PLEASE HELP ME WITH THIS PROBLEM: 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 da

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: PLEASE HELP ME WITH THIS PROBLEM: 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 da      Log On


   

Question 55172: PLEASE HELP ME WITH THIS PROBLEM:
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 funmath(2933) About Me  (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 highlight%28P=100e%5Ert%29 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.
P=200 and 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 Use this rule to rewrite the equation: highlight%28ln%28a%5Em%29=mln%28a%29%29
ln%282%29=3rln%28e%29 Remember this rule highlight%28ln%28e%29=1%29
ln%282%29=3r%281%29
ln%282%29=3r
%28ln%282%29%29%2F3=3r%2F3
%28ln%282%29%29%2F3=r
.6931471806%2F3=r You need a scientific calculator for that.
.2310490602=r
Round off to wherever your asked.
Happy Calculating!!!