SOLUTION: In the absence of predators, the natural growth rate of rabbits is 4% per year. A population begins with 100 rabbits. The function f(x) = 100(1.04)^x gives the population of rabb

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: In the absence of predators, the natural growth rate of rabbits is 4% per year. A population begins with 100 rabbits. The function f(x) = 100(1.04)^x gives the population of rabb      Log On


   

Question 968704: In the absence of predators, the natural growth rate of rabbits is
4% per year. A population begins with 100 rabbits. The function
f(x) = 100(1.04)^x gives the population of rabbits in x years.
a. How long will it take the population of rabbits to double?
b. How long will it take the population of rabbits to reach 1000?
Found 2 solutions by josgarithmetic, amarjeeth123:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
HOW LONG would it take:

200=100%281.04%29%5Ex
2=1.04%5Ex
Pick whichever base you prefer.
ln%282%29=ln%281.04%5Ex%29
ln%282%29=x%2Aln%281.04%29
highlight%28x=ln%282%29%2Fln%281.04%29%29 which is approximately 17%262%2F3 years.

The second question's solution works similarly.

Answer by amarjeeth123(570) About Me  (Show Source):
You can put this solution on YOUR website!
a.For the population to double we have 100(1.04)^x=200
(1.04)^x=2
Taking logarithm on both sides to base 10 we get,
x log(1.04)=log2
x=log2/log(1.04)=17.67 years
It will double in 17.67 years.
b.For the population to become 1000 we have 100(1.04)^x=1000
(1.04)^x=10
Taking logarithm on both sides to base 10 we get,
x log(1.04)=log 10
x log(1.04)=1
x=1/log(1.04)=58.708 years.
It will become 1000 in 58.708 years.