Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as many rabbits as the year before. How many rabbits were there after x years? Write a function to represent this scenario.

Answer 1

To represent the scenario of rabbit population growth over the years, you can use an exponential function.

Initially, at year 0, there are 6 rabbits. Each year, the number of rabbits quadruples (four times as many as the year before).

This situation can be modeled with the following function:

\[ R(x) = 6 \times 4^x \]

Where:

• \( R(x) \) is the number of rabbits after \( x \) years,
• \( 6 \) is the initial number of rabbits,
• \( 4 \) is the growth factor (since the rabbit population quadruples each year),
• \( x \) is the number of years.

So, after \( x \) years, you can find out how many rabbits there are by substituting the value of \( x \) into the function.