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?

Answer 1

@campbell_st

Answer 2

Last question I promise!

Answer 3

@Hero

Answer 4

sorry I have to go to school.

Answer 5

okay no problem!

Answer 6

@dan815

Answer 7

@perl

Answer 8

@bpstation

Answer 9

okay...

Answer 10

okay...

Answer 11

that looks familiar

Answer 12

so I got the answer .169 which rounds to be 17%?

Answer 13

wait what?

Answer 14

the original function was , after 1 year you have 2*3^1

Answer 15

ohhh okay

Answer 16

there isn't a typo. I am positive of that

Answer 17

that equation that you have here is the exponential growth formula

Answer 18

which is correct

Answer 19

the first equation should have a 7x on the outside

Answer 20

right, if we want to keep x as number of years

Answer 21

3 to the 1/7th power is the same thing as the 7th root of 3

Answer 22

right?

Answer 23

right

Answer 24

so when it is simplified it would be f(x)=2(1.17)^7x

Answer 25

$$\Large f(x) = 2\left( 3^x \right) = 2\left( 3^{1/7} \right)^{7x} = $$

Answer 26

I am trying to find r in the exponential growth equation which is A=P(1+r)^t

Answer 27

1.17=1+r

Answer 28

and r is the rate

Answer 29

1.17 = 1 + r

1 .17 - 1 = r

Answer 30

so then you solve for r and you get 17% when rounded

Answer 31

right?

Answer 32

so the answer would be B

Answer 33

correct

Answer 34

Great, thanks!