Solve the problem.
12) The rabbit population in a forest area grows at the rate of monthly. If there are 150 rabbits in September, find
how many rabbits (rounded to the nearest whole number) should be expected by next September. Use
t

To find the expected rabbit population by next September, we will use the formula for exponential growth. Given that the growth rate is per month, the monthly growth factor is . The time from September of one year to September of the next year is months.

Using the formula , we calculate:

Calculating this gives approximately:

Rounding to the nearest whole number, the expected population is rabbits.

In the context of population modeling, it’s fascinating to note how even a small growth percentage can lead to significant increases over time. This exponential growth means that if you have a pair of rabbits, a few years down the line you could potentially have hundreds of them, taking over the forest!

To prevent common pitfalls when working with growth rates, it’s essential to ensure you’re applying the correct formula and understanding the base growth factor. Sometimes confusion arises when miscalculating the exponent for the time period, so double-checking your monthly rate and the number of months involved can save you from graphs that should show a booming population but instead reveal a population crash!