2009-10-18, 06:35 PM
Oh joy. We just came to my most favorite chapter in AP Environmental Science! (sarcasm) Anyway I'm good with every question I've been presented with so far except this one:
3) Given a growth rate of 3 percent per year, how long will it take for a population of 100,000 individuals to double? How long will it take to double when the population reaches 10 million?
My teacher said in order to solve it, you have to use one of the two mathematical growth formulas, either exponential or logistic.
Exponential: dN/dt = rN, that is,the change in the number of individuals (dN) per change in time (dt) equals the rate of growth ® times the number of individuals in the population (N).
Logistic: dN/dt = rN(1- N/K), where the change in numbers over time (dN/dt) equals the exponential growth rate (rN) times the portion of the carrying capacity (K) not already taken by the current population size (N).
This is the thing though, there is no given carrying capacity in the question so I assumed that using the logistic equation was not an option, until I remembered that exponential growth has no limits. >.< Advice on how to solve this question would be appreciated.
3) Given a growth rate of 3 percent per year, how long will it take for a population of 100,000 individuals to double? How long will it take to double when the population reaches 10 million?
My teacher said in order to solve it, you have to use one of the two mathematical growth formulas, either exponential or logistic.
Exponential: dN/dt = rN, that is,the change in the number of individuals (dN) per change in time (dt) equals the rate of growth ® times the number of individuals in the population (N).
Logistic: dN/dt = rN(1- N/K), where the change in numbers over time (dN/dt) equals the exponential growth rate (rN) times the portion of the carrying capacity (K) not already taken by the current population size (N).
This is the thing though, there is no given carrying capacity in the question so I assumed that using the logistic equation was not an option, until I remembered that exponential growth has no limits. >.< Advice on how to solve this question would be appreciated.