Question

@ganeshie8, The function f(x) = 14(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 117%

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

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

Answer 1

any ideas?

Answer 2

ucf ftw! but no i dont know

Answer 3

going with D

Answer 4

No, D's incorrect.

\[\large f(x) = 14 \times 3^x\] ^ ^
| |_ growth rate
inititial value

The old growth rate was 3 = 300%, with an initial value = 14.

The new growth rate is going to be \[\large \sqrt[7]{3} \approx 1.17 = 117\%\]with the new inital value \[\frac{ 14 }{ 7} = 2\]Thus the new function is
\[y = 2 \times 1.17^x, \space growth \space rate \space 117\%\]