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?
a) f(x) = 16(2)x; growth rate 200%
b) f(x) = 16(2)2x; growth rate 8%
c) f(x) = 16(1.41)x; growth rate 8%
d) f(x) = 16(1.41)2x; growth rate 41%
because she wants to go from once a year to twice a year the (2) needs to be raised to the 1/2 power and x needs to be multiplied by the number of times per year
so you get 16(2^1/2)2x
2^1/2 = 1.41
so f(x) = 16(1.41)2x
the only answer that has the correct equation is D
