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Yuri [45]
1 year ago
15

When rabbits were introduced to the continent of Australia they quickly multiplied and spread across the continent since there w

ere 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.

Mathematics
1 answer:
stepan [7]1 year ago
3 0

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}=\frac{770}{6}

b^{}=\sqrt[3]{\frac{309}{32}}undefined

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