Question

1. a tree frog population doubles every three weeks. currently there are 10 tree frogs in a park. how many tree frogs will there be in 6 months, assuming there are four weeks in each month?

Explanation:

Step1: Calculate total weeks

First, find total weeks in 6 months.
$6 \text{ months} \times 4 \text{ weeks/month} = 24 \text{ weeks}$

Step2: Find doubling periods

Determine how many 3-week periods fit in 24 weeks.
$\frac{24}{3} = 8 \text{ doubling periods}$

Step3: Apply exponential growth formula

Use the formula for exponential growth: $P = P_0 \times 2^n$, where $P_0$ is initial population, $n$ is number of doubling periods.
$P = 10 \times 2^8$

Step4: Compute final population

Calculate $2^8$ and multiply by 10.
$2^8 = 256$, so $P = 10 \times 256 = 2560$

Answer:

2560