Question

The function f(x) = 16(2)x represents the growth of a bee population every year in a remote swamp. Jennifer wants to manipulate the formula to an equivalent form that calculates two times a year, not just once a year. Which function is correct for Jennifer's purpose, and what is the new growth rate?

Answer 1

The function f(x) = 16
`(2)^x` represents the growth of a bee population every year in a remote swamp.

Jennifer want to calculate twice a year so we change 2 to
`2^(1)/(2)`. Also we multiply x by 2

f(x) = 16
`(2)^x`

f(x) =
`16(2^(1)/(2))^(2x)`

`2^(1)/(2) is 1.414`

f(x)= 16
`(1.414)^(2x)`

The function for Jennifer's purpose is f(x)= 16
`(1.414)^(2x)`

We know y= a(1+r)^t is exponential growth

where 'r' is the growth rate

From the function we got 1 + r= 1.414

1 + r = 1.414

r = 0.414

Now we multiply by 100

So r= 41%

So growth rate = 41%