Question

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp. Jackie wants to manipulate the formula to an equivalent form that calculates three times a year, not just once a year. Which function is correct for Jackie's purpose, and what is the new growth rate? (5 points)


f(x) = 4(4)x; growth rate 400%
f(x) = 4(4)3x, growth rate 4%
f(x) = 4(1.59)3x; growth rate 59%
f(x) = 4(1.59)x; growth rate 4%

Answer 1

What is f(x) equal to? What is 4(4)x?

Answer 2

I think it would be B.

Answer 3

they are exponential as well the answers sorry for the typo

Answer 4

rearrange the exponent as \(\frac{3x}{3}\) and simplify :

\[\large{\begin{align}f(x)=4(4)^x &= 4(4)^{\frac{3x}{3}}\\~\\
&= 4(4^{\frac{1}{3}})^{3x}\\~\\
&= ?
\end{align}}\]

Answer 5

ok

Answer 6

use ur calculator to work \(\large 4^{\frac{1}{3}}\)

Answer 7

16.3

Answer 8

nope, try again

Answer 9

wolf says \(\approx 1.59\)
http://www.wolframalpha.com/input/?i=4%5E%281%2F3%29

Answer 10

ah

Answer 11

So the answer would be D?

Answer 12

or C.

Answer 13

c would be the answer

Answer 14

right, one of them
how do we pin down which one it is

Answer 15

it is c?

Answer 16

how do you know

Answer 17

because it is the same but manipulatd as the original equation

Answer 18

rearrange the exponent as \(\frac{3x}{3}\) and simplify :

\[\large{\begin{align}f(x)=4(4)^x &= 4(4)^{\frac{3x}{3}}\\~\\
&= 4(4^{\frac{1}{3}})^{3x}\\~\\
&= 4(1.\color{red}{59})^{3x}\\~\\
\end{align}}\]

that red part gives you the growth rate

Answer 19

oh ok.

Answer 20

the fly population grows at a rate of \(59\%\) per quarter

Answer 21

we know c is the anser because 59 percent is the growht rate

Answer 22

?

Answer 23

yes ?

Answer 24

yes

Answer 25

.