Question

The function f(x) = 2(3)x represents the growth of a dragonfly population every year in a remote swamp. Rose wants to manipulate the formula to an equivalent form that calculates seven times a year, not just once a year. Which function is correct for Rose's purpose, and what is the new growth rate?


f(x) = 2(3)x; growth rate 200%

f(x) = 2(1.17)7x; growth rate 17%

f(x) = 2(3)x, growth rate 2%

f(x) = 2(1.17)x; growth rate 2%

Answer 1

please help

Answer 2

okay just sit there then

Answer 3

\[f(x) = 2(3)^x = 2(3)^{7x/7} = 2((3)^{1/7})^{7x} = 2(1.17)^{7x}
\]Growth rate: \[ 2(1.17)^{7x} = 2(1 + 0.17)^{7x}\]Growth rate = 0.17 or 17%