Question

When rabbits were introduced to the continent of Australia they quickly multiplied and spread across the continent since there were only primitive marsupial competitors and predators to interfere with the exponential growth of their population. The data in the following table can be used to create a model of rabbit population growth

Answer 1

Given the first term at t₀ is 6 and the second term at t₃ is 32, let's take rabbit population as a function of time to be:

y = abˣ

where y is the population at time x and a the initial population at t₀

32 = 6b³

b = 1.75

Now we replace b in the population function:

y = 6(1.75)ˣ regression for the rabbit population as a function of time x.

The exponential function in terms of base is usually expressed as:

A = A₀e^kt

Hence, the regression equation in terms of base e is:

We substitute en last function, y - value with any number higher than 10,000 to estimate the time for the rabbits to exceed 10,000.

Hence, it takes approximately 13.3 months for the population to exceed 10000