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Amara monitored a cockroach infestation in an abandoned warehouse over time. The table shows the cockroach population every week.

Create a recursive function that models this situation in terms of \( n \) weeks that have passed.

Enter the correct answer in the box.

Answer :

The recursive function f(n) = 6 * f(n-1), with f(1) = 5, models the cockroach population over n weeks, reflecting the observed exponential growth pattern.

To model the cockroach population over time, we observe a pattern where the number of cockroaches increases each week. Looking at the provided data, we notice that each week, the population is multiplied by a factor of 6. For example, in week 2, the population is 5 * 6 = 30, and in week 3, it is 30 * 6 = 180. This suggests an exponential growth pattern.

We can express this growth using a recursive function, where each term is obtained by multiplying the previous term by the growth factor (6). Let's denote the number of cockroaches in week n as f(n).

f(n) = 6 * f(n-1)

where f(1) = 5 (initial population).

This recursive function captures the exponential growth of the cockroach population over time, as each week, the population is multiplied by a factor of 6.

In summary, the recursive function f(n) = 6 * f(n-1), with f(1) = 5, models the cockroach population over n weeks, reflecting the observed exponential growth pattern.

The question probable may be:

Amara monitored a cockroach infestation in an abandoned warehouse over time. The table shows the cockroach population every week. Create a recursive function f(n) that models this situation in terms of n weeks that have passed. Enter the correct answer in the box.

No. of weeks no. of cockroaches

1 5

2 30

3 180

4 1080

5 6480

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