Question

A population of rabbits triples every year. If the population size is 12 rabbits after the 1st year, how many will there be after 7 years?

Answer 1

To find the population of rabbits after 7 years, we start with the information that the population triples every year. Given that the population after the first year is 12 rabbits, we can express the population after each subsequent year mathematically.

Let \( P(n) \) represent the population after \( n \) years. Since the population triples each year, we can express this as:

\[
P(n) = P(n-1) \times 3
\]

Since we know \( P(1) = 12 \), we can calculate the population for the next years:

- After year 2:
\[
P(2) = P(1) \times 3 = 12 \times 3 = 36
\]

- After year 3:
\[
P(3) = P(2) \times 3 = 36 \times 3 = 108
\]

- After year 4:
\[
P(4) = P(3) \times 3 = 108 \times 3 = 324
\]

- After year 5:
\[
P(5) = P(4) \times 3 = 324 \times 3 = 972
\]

- After year 6:
\[
P(6) = P(5) \times 3 = 972 \times 3 = 2916
\]

- After year 7:
\[
P(7) = P(6) \times 3 = 2916 \times 3 = 8748
\]

Therefore, the population of rabbits after 7 years will be \( \boxed{8748} \).