Question

a community of rabbits begins with an initial population of 96 and grows 7% per month. make a table that shows the population for each of the next 15 months. based on the table, find the doubling time of the population and briefly discuss how well the approximate doubling time formula works for this case.

complete the table below for months 0 through 7.
(round to the nearest whole number as needed.)
\

$$\begin{tabular}{|c|c|} \\hline month & population \\\\ \\hline 0 & 96 \\\\ \\hline 1 & \\\\ \\hline 2 & \\\\ \\hline 3 & \\\\ \\hline 4 & \\\\ \\hline 5 & \\\\ \\hline 6 & \\\\ \\hline 7 & \\\\ \\hline \\end{tabular}$$

Explanation:

Model the population growth

Using the Exponential Growth knowledge point

$$ P(t) = P_0 \times (1 + r)^t = 96 \times (1.07)^t $$

Calculate the population values

Using the Exponential Growth knowledge point

$$
LATEXBLOCK0
$$

Determine the doubling time

Using the Doubling Time knowledge point

$$
LATEXBLOCK1
$$

The population doubles between month 10 and month 11 (approximately 10.24 months).

Compare with the approximate formula

Using the Rule of 70 knowledge point

$$ T_{\text{double}} \approx \frac{70}{7} = 10 \text{ months} $$

The approximation of 10 months is very close to the actual doubling time of approximately 10.24 months.

Answer:

Month	Population
1	103
2	110
3	118
4	126
5	135
6	144
7	154