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. Time (months)036912No. of Rabbits6321073097701. Find the regression equation for the rabbit population as a function of time x.2. Write the regression equation in terms of base e.3. Use the equation from part b to estimate the time for the rabbits to exceed 10,000.

Answer 1

Given:

We get the points (0,6), (3,32), and (12,770) from the given table.

1.

Let y be the number of the rabbit and x be the number of months.

Consider the regression equation of the form.

`y=a(b)^x`

Substitue x=0 and y=6 in the equation, we get

`6=ab^0`

`a=6`

Substitue x=12 and y=770 in the equation, we get

`770=ab^(12)`

`\text{ Substitute }a=6\text{ in the equation, we get}`

`b^(12)=(770)/(6)`

`b^{}=\sqrt[3]{(309)/(32)}`