Question

A population of rabbits, in the absence of other factors, grows at a rate proportional to the current population: specifically, it triples every 2 years. There is another factor, however: foxes kill 2 rabbits per month. Supposing there are 100 rabbits initially. Write down the initial value problem you would solve to find the population of rabbits at any given time.

Answer 1

G = kX

Where:

G - Growth rate

X = the initial/current population of rabbit

k = is the constant of proportionality.

Explanation:

As we are told in the question, the growth rate is proportional to the current population. This information gives us the initial value needed to solve to find the population of rabbits at any given time.

Other information given as needed for computation and we are not asked to do anything further.

Analytically,

If X = 100

And it triples in 2 years. That is, 3*X = 300. 2 years is 24 months.

This gives us the monthly growth rate = 300/24 = 12.5 => 12 to 13 rabbits per months.

Foxes kill 2 rabbits per month. This implies that 2*24 = 48 rabbits are killed by Foxes in 24 months.

By implication, the population of rabbits in 2 years will be

X (in 2 years) = 300 - 48 = 252 rabbits.