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?

Answer 1

@dtan5457

Answer 2

can you help me with this step by step?

Answer 3

@jim_thompson5910

Answer 4

what does x represent?

Answer 5

x=times during the year?

Answer 6

so in this case x=3 ? right?

Answer 7

@jim_thompson5910

Answer 8

x is the number of years

Answer 9

so if x = 3, then that represents year 3

Answer 10

so i would plant this like:
f(3)=4(4)^3 ?

Answer 11

how do we adjust things so it calculates 3 times a year

Answer 12

nope

Answer 13

we multiply by 3 so they would adjust?

Answer 14

@jim_thompson5910

Answer 15

yes x would turn into 3x

Answer 16

so the function would now be
f(x)=4(4)^3x ?

Answer 17

yes \[\Large f(x) = 4(4)^{3x}\]

Answer 18

so i would solve this function?

Answer 19

@jim_thompson5910

Answer 20

what do you mean?

Answer 21

oh wait nevermind lol we dont solve it . i just saw my options lol

Answer 22

so would f(x)=4(4)^3x would be my final answer? amd the rate percentage would be 4% ?

Answer 23

@jim_thompson5910

Answer 24

can i see a screenshot of all the options?

Answer 25

yes here it is

Answer 26

@jim_thompson5910

Answer 27

ok let me think

Answer 28

ok , to find the rate id think of graphing it, but when i graph its like a really straight line

Answer 29

\[\Large e^{kx} = 4^{3x}\]
\[\Large \ln(e^{kx}) = \ln(4^{3x})\]
\[\Large kx*\ln(e) = 3x*\ln(4)\]
\[\Large k*1 = 3*\ln(4)\]
\[\Large k = 3*\ln(4)\]
\[\Large k \approx 4.15888\]
So the growth rate is approximately 4%

Answer 30

so yes, it is B

Answer 31

what was the formula you used to solve for the rate? is it the average rate of change formula?

Answer 32

@jim_thompson5910

Answer 33

I set e^(kx) equal to 4^(3x) and solved for k

Answer 34

thank you so much :)

Answer 35

np