Question

Suppose a population of 40 crickets doubles in size every month. The function f(x)=40⋅2x
gives the population after x
months. How many crickets will there be after 3 years? (1 point)
Responses

2,880
2,880

240
240

320
320

2,748,779,069,440

Answer 1

To find the population of crickets after 3 years, we first convert the time from years to months. Since there are 12 months in a year, 3 years is:

3 years × 12 months/year = 36 months

Now we can use the function \( f(x) = 40 \cdot 2^x \) to calculate the population after 36 months:

\[
f(36) = 40 \cdot 2^{36}
\]

Calculating \( 2^{36} \):

\[
2^{36} = 68,719,476,736
\]

Now, we can calculate:

\[
f(36) = 40 \cdot 68,719,476,736
\]

\[
f(36) = 2,748,779,069,440
\]

Therefore, the population of crickets after 3 years will be **2,748,779,069,440**.

So the correct response is:

**2,748,779,069,440**.