SOLUTION: Please help me with this problem.I am having a lot of issues with these types of problems.I tried plugging in 200 for P and 3 for t but I still cant get it right. The population

Question 79656: Please help me with this problem.I am having a lot of issues with these types of problems.I tried plugging in 200 for P and 3 for t but I still cant get it right.
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 the number of days since the original population is expected to reach 200 in 3 days.
a. 0.231
b. 0.549
c. 1.098
d. 1.50
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 the number of days since the original population is expected to reach 200 in 3 days.
:
100(e^rt) = P
:
Substitute for t and P
100(e^(3r)) = 200
:
Divide both sides by 100 and you have:
e^(3r) = 2
:
Find nat log of both sides:
ln(e^3r) = ln(2)
:
3r*ln(e) = ln(2); log equiv of exponents
:
3r = .693147; remember ln(e) = 1
:
r = .693147/3
:
r = .231
:
:
Check solution with a good calc: enter 100(e^(.231*3)) = 199.97 ~ 200
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