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

I might be wrong but i think it’s the second one

Answer 2

Answer : option B

The function
`f(x)= 2(3)^x` represents the growth of a dragonfly population every year.

Rose wants to manipulate the formula to an equivalent form that calculates seven times a year, not just once a year. So function becomes

`f(x)= 2(3^(1)/(7))^(7x)`

In exponential function ,
`f(x) = a(1+r)^x`, where 'r' is the growth rate

`f(x)= 2(1.17)^(7x)`

1 + r = 1.17

r = 0.17

So growth rate = 0.17= 17%

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