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.

\

$$\begin{tabular}{|c|c|} \\hline 9 & 176 \\\\ \\hline 10 & 189 \\\\ \\hline 11 & 202 \\\\ \\hline 12 & 216 \\\\ \\hline 13 & 231 \\\\ \\hline 14 & 248 \\\\ \\hline 15 & 265 \\\\ \\hline \\end{tabular}$$

based on previously calculated data, determine the doubling time of the population.

the doubling time of the population is between 10 and 11 months.
(type a whole number. use ascending order.)

briefly discuss how well the approximate doubling time formula works for this case. choose the correct answer below.

a. the doubling time formula works well to approximate the doubling time because the formula always works correctly.
b. the doubling time formula does not work well to approximate the doubling time because the growth rates are too large.
c. the doubling time formula works well to approximate the doubling time because it is accurate to the computed values.
d. the doubling time formula does not work well to approximate the doubling time because the growth rates are too small.

Explanation:

Determine the actual doubling time from the table

Using the Doubling Time knowledge point

$$
LATEXBLOCK0
$$

Apply the approximate doubling time formula

Using the Rule of 70 knowledge point

$$
LATEXBLOCK1
$$

Evaluate the formula's performance

Using the Doubling Time and Rule of 70 knowledge points

$$
LATEXBLOCK2
$$

The approximation is highly accurate compared to the computed values.

Answer:

Question 1

The doubling time of the population is between <blank>10</blank> and <blank>11</blank> months.

Question 2

• A. The doubling time formula works well to approximate the doubling time because the formula always works correctly.
• B. The doubling time formula does not work well to approximate the doubling time because the growth rates are too large.
• C. The doubling time formula works well to approximate the doubling time because it is accurate to the computed values. (Correct answer)
• D. The doubling time formula does not work well to approximate the doubling time because the growth rates are too small.