Continuous compounding question

Question

A population of rabbits starts out with $100$ rabbits. The growth rate is $11.7$% per day. Determine the exponential equation.

Is it $$\mathbb {P(t)} = 100e^{11.7t}$$

Can you guys give me the answer, I have a test tomorrow.

Answer 1

Hint: If time is measured in days (and the model is correct, which it isn't), the population after $t$ days is $100 (1.117)^t$. You may want to express this as $100e^{kt}$ for suitable $k$. Use logarithms to the base $e$ to find $k$.

Answer 2

Hint You are given $P(0)=100$. With a growth rate of $11.7\%$, you should have $P(1) = 111.7 \approx 112$. Does your equation yield these results for $t=0$ and $t=1$? If not, what needs to be changed?