MATH SOLVE

4 months ago

Q:
# 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%

Accepted Solution

A:

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 2f(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 growthwhere 'r' is the growth rateFrom the function we got 1 + r= 1.4141 + r = 1.414r = 0.414Now we multiply by 100So r= 41%So growth rate = 41%