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 $2^\frac{1}{2}$. Also we multiply x by 2

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

f(x) = $16(2^\frac{1}{2})^{2x}$

$2^\frac{1}{2} is 1.414$

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%