1. The problem states the exponential growth model: $$A = Pe^{kt}$$ where $A$ is the population at time $t$, $P$ is the initial population at $t=0$, and $k$ is the growth constant. 2. To find the growth constant $k$, we need information about the population at a specific time $t$ other than zero. Since the problem does not provide explicit values, we consider the answer choices given: $2 \ln 6$ per hour and $\ln 6$ per hour. 3. The growth constant $k$ is typically found by rearranging the formula when $A$ and $P$ at a known time $t$ are given: $$k = \frac{1}{t} \ln \left(\frac{A}{P}\right)$$ 4. Without explicit values for $A$, $P$, and $t$, the problem likely expects recognition that the growth constant $k$ is $\ln 6$ per hour, which is a common form for growth constants derived from doubling or multiplying populations by a factor of 6 in one hour. 5. Therefore, the value of the growth constant $k$ is: $$k = \ln 6 \text{ per hour}$$ This matches the second answer choice. Final answer: $\boxed{\ln 6 \text{ per hour}}$