Question

During the 19th century, rabbits were brought to Australia. Since the rabbits had no natural enemies on that continent, their population increased rapidly. Suppose there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.

Assume that the rabbit population continued to grow at that rate. Estimate the Australian rabbit population in 1872.

Short answer

The rabbit population continued to grow at that rate, the Australian rabbit population in 1872 is22935416899.

Step-by-step solution

Step 1. Given Information.

Given, during the 19th century, rabbits were brought to Australia. Since the rabbits had no natural enemies on that continent, their population increased rapidly. Suppose there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.

An exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is $y=65000{\left(\sqrt{\frac{500}{13}}\right)}^x$

Assuming that the rabbit population continued to grow at that rate, the Australian rabbit population in 1872 is to be determined.

Step 2. Explanation.

For 1872,

$\begin{array}{l}x=1872-1865\\ x=7\end{array}$

Plugging the value in the equation:

$\begin{array}{l}y=65000{\left(\sqrt{\frac{500}{13}}\right)}^x\\ y=65000{\left(\sqrt{\frac{500}{13}}\right)}^7\\ y=65000\left(352852.57\right)\\ y=22935416899\end{array}$

Step 3. Conclusion.

Hence the rabbit population continued to grow at that rate, the Australian rabbit population in 1872 is 22935416899.