Question

Suppose the function f(x)=30(2)^x gives a beetle population after x weeks.How many beetles will there be after 56 days

Answer 1

7,680 beetles

Step-by-step explanation:

The function that gives the beetle population after x weeks is given below:

`f\mleft(x\mright)=30\mleft(2\mright)^x`

To determine the beetle population after 56 days, first convert 56 days to weeks.

`56\text{ days=}(57)/(7)=8\text{ we}eks`

Thus, the beetle population will be:

`\begin{gathered} f(8)=30(2)^8 \\ =30*256 \\ =7,680 \end{gathered}`

There will be 7,680 beetles after 56 days.