The function f(x) = 16[tex] (2)^x [/tex] 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 [tex] 2^\frac{1}{2} [/tex]. Also we multiply x by 2
f(x) = 16[tex] (2)^x [/tex]
f(x) = [tex] 16(2^\frac{1}{2})^{2x} [/tex]
[tex] 2^\frac{1}{2} is 1.414 [/tex]
f(x)= 16[tex] (1.414)^{2x} [/tex]
The function for Jennifer's purpose is f(x)= 16[tex] (1.414)^{2x} [/tex]
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%
