Question

A) Suppose a population of 40 crickets doubles in size every month. The function

f(x) = 40.2 gives the population after 2 months. How many crickets will there be after 3 years? (1 point)

© 2,880

240

320

2,748,779,069,440

Answer 1

To calculate the population of crickets after 3 years, we need to start with the initial population and apply the doubling rate.

Given:
- Initial population = 40 crickets
- The population doubles every month.

First, we need to determine the total number of months in 3 years:
\[
3 \text{ years} = 3 \times 12 \text{ months} = 36 \text{ months}
\]

Now, we use the formula for exponential growth where the population doubles:
\[
P(t) = P_0 \times 2^{t}
\]
where:
- \( P(t) \) = population at time \( t \)
- \( P_0 \) = initial population
- \( t \) = number of months

Now substituting the values:
\[
P(36) = 40 \times 2^{36}
\]

Calculating \( 2^{36} \):
\[
2^{36} = 68,719,476,736
\]

Now multiply this by the initial number of crickets:
\[
P(36) = 40 \times 68,719,476,736
\]
Calculating the final result:
\[
P(36) = 2,748,779,069,440
\]

So, the population of crickets after 3 years is **2,748,779,069,440**.

The correct answer is:
**2,748,779,069,440**