Question

Suppose a population of 140 crickets doubles in size every month. The function f(x) = 140*2* gives the population after x months. How many crickets will there be after 2 years?

Answer 1

`f(x)\text{ = }2348810240\text{ crickets (option D)}`

Step-by-step explanation:

`\begin{gathered} \text{The function:} \\ f(x)\text{ = 140}*2^x \\ \text{where x = number of months} \end{gathered}`
`\begin{gathered} x\text{ =2 years} \\ 12\text{ months = 1 year} \\ 2\text{ years = 2(12) = 24 months} \end{gathered}`
`\begin{gathered} f(x)\text{ = 140 }*2^(24) \\ f(x)\text{ = 140 }*\text{ 16777216} \\ f(x)\text{ = }2.34881024\text{ }*10^9 \\ f(x)\text{ = }2348810240\text{ crickets (option D)} \end{gathered}`