The problem describes a population of cottontail rabbits that doubles every 12 years. We are given the initial population (56) and a target population (149). We need to find the number of years it takes for the population to reach the target population.

1. Problem Description

The problem describes a population of cottontail rabbits that doubles every 12 years. We are given the initial population (56) and a target population (149). We need to find the number of years it takes for the population to reach the target population.

2. Solution Steps

The formula for exponential growth is given by:

$P(t) = P_0 * 2^{(t/d)}$

Where:

$P(t)$ is the population at time $t$

$P_0$ is the initial population

$t$ is the time elapsed

$d$ is the doubling time

In this problem, we have:

$P_0 = 56$

$P(t) = 149$

$d = 12$

We need to find $t$.

$149 = 56 * 2^{(t/12)}$

Divide both sides by 56:

$\frac{149}{56} = 2^{(t/12)}$

Take the natural logarithm of both sides:

$ln(\frac{149}{56}) = ln(2^{(t/12)})$

Use the logarithm property $ln(a^b) = b*ln(a)$:

$ln(\frac{149}{56}) = \frac{t}{12} * ln(2)$

Solve for $t$:

$t = \frac{12 * ln(\frac{149}{56})}{ln(2)}$

$t = \frac{12 * ln(2.6607)}{ln(2)}$

$t = \frac{12 * 0.9788}{0.6931}$

$t = \frac{11.7456}{0.6931}$

$t \approx 16.946$

Round to the nearest hundredth:

$t \approx 16.95$

3. Final Answer

16.95