a local community of a rock chucks in Wyoming that are increasing at a rate of 11% per month how many months tell their population doubles and quadruples?

Question

I need help with this question on my homework. It is stumping me. 

Answer 1

For population growth we have the formula   P = P₀e^rt

P = future or final population

P₀=initial population

r = rate of growth = 11% = .11

t = time in years

 

We want to know when P = 2P₀

 

2P₀ = P₀e^.11t

Divide both sides by P₀

2 = e^.11t

 

Take ln of both sides

 

ln2 = ln(e^.11t)

ln2 = .11t(ln e)

Note that ln e = 1

ln2 = .11t

t = ln2/.11 = 6.3 years

 

(6.3 years)(12 mos/yr) = 75.6 months or approximately 76 months

*****************************************************

For the population to quadruple we use the same formula

 

4P₀ = P₀e^.11t

4 = e^.11t

ln4 = ln(e^.11t)

ln 4 = .11t ln e

ln 4 = .11t

t = ln4/.11

 

t = 12.6 years

(12.6 years)(12 mos/yr) = 151.2 months

 

The population will quadruple in approximately 151 months