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.
:
 100*e^(rt) = P
:
Substitute for t and P
100*e^(3r) = 200
:
Divide both sides by 100:
e^(3r) = 200/100
e^(3r) = 2
:
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
:
:
Check solution on a good calc: enter e^(3*.23105) = 2.0000