SOLUTION: How long will it take for the population of a certain country to double if its annual growth rate is 3.5% (round to the nearest year). Use the exponential growth model P(t) = P su

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How long will it take for the population of a certain country to double if its annual growth rate is 3.5% (round to the nearest year). Use the exponential growth model P(t) = P su      Log On


   

Question 282911: How long will it take for the population of a certain country to double if its annual growth rate is 3.5% (round to the nearest year). Use the exponential growth model P(t) = P subscript 0 e^kt.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P=P0%2Ae%5E%28kt%29
In one year, P will grow to 1.035*P0.
Use this to find k.
1.035%2AP0=P0%2Ae%5E%28k%29
e%5Ek=1.035
k=ln%281.035%29
Now to find the time to double, let P=2*P0.
2%2AP0=P0%2Ae%5E%28kt%29
e%5E%28kt%29=2
kt=ln%282%29
t=ln%282%29%2Fk=ln%282%29%2Fln%281.035%29
That's the exact answer.
Approximately,
t=20.15+
About 20 years and 2 months.