# Continuous compounding 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.

• 11.7% means 0.117; so $\mathbb {P(t)} = 100e^{0.117t}$ could be better but I do not think that this is the best way to formulate the problem. Give attention to what André Nicolas wrote in his comment. – Claude Leibovici Feb 18 '14 at 6:24

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 $k$.
• Then use the hint. Equivalently, $100e^{(k)(1)}=111.7$, so $e^k=1.117$ so $k=\ln(1.117)\approx 0.11064652$. – André Nicolas Feb 18 '14 at 4:03
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?
• Your function is right but the coefficient is wrong. After one day, $e^{0.117}$ is $1.12412$ which means an increase of 12.24%. Use what André Nicolas wrote and you are done. – Claude Leibovici Feb 18 '14 at 6:40