Question

@myininaya I know what I need to do and all but I just need you to tell me if I'm on the right path and if not then I will just look over on the word problem and see what I did wrong. A local snail population grows according to the function g(x) = 200(1.03)2x. Demonstrate the steps to convert g(x) into an equivalent function with only x as the exponent.

Answer 1

@myininaya if you can, please come

Answer 2

\[g(x)=200(1.03)^{2x}?\]

Answer 3

ok so I have an idea on how im supposed to do this so I want you to tell me if im on the right path. Ok?

Answer 4

do you know law of exponents ?

Answer 5

alright

Answer 6

shoot

Answer 7

So what I think I need to do is go and multiply 1.03 and 2, then with 200

Answer 8

is it ok? if not i will go over.

Answer 9

well Kay let me remind of one particular law we will need for this

Answer 10

\[(a^{xy})=(a^y)^x \]

Answer 11

pretend y is 2 if you want

Answer 12

? so i have to multiply 1.03 by 2 and that's it or is it more complicated than that.

Answer 13

no something like a^2 means a*a

Answer 14

not 2*a

Answer 15

\[g(x)=200(1.03)^{2x} \\ g(x)=200(1.03^2)^x\]

Answer 16

1.03^2=?

Answer 17

ohh

Answer 18

yeah i forgot that it is an exponent not just a number so it would be 1.03 * 1.03

Answer 19

yes for the base yes

Answer 20

then by 200 and my answer would be there

Answer 21

right?

Answer 22

well 200 is on the outside

Answer 23

you just need to do this:
\[g(x)=200(1.03)^{2x} \\ g(x)=200(1.03^2)^x \\ g(x)=200(1.03 \cdot 1.03)^x\]

Answer 24

unless g was meant to be the following:
\[g(x)=(200 \cdot 1.03)^{2x}\]?

Answer 25

oh yeah cuz I did not know if i wasd supposed to leave it like that or multiply by 200 afterwards. That's why i wanted someone to go over my original thoughts

Answer 26

yep the only step you need to do is do the 1.03*1.03

Answer 27

you cannot do anything with the 200 because it is outside the ( )^x part

Answer 28

so you will just bring it down

Answer 29

\[g(x)=200(?)^x\]
what did you get for the question mark

Answer 30

well thanks for checking.

Answer 31

ill tell you... 1.0609

Answer 32

that's good
once you replace that ? with that number you are done

Answer 33

don't do anything else

Answer 34

\[g(x)=200(1.0609)^x \]

Answer 35

thank you, i gave you a medal

Answer 36

I gave you a medal for your effort and wanting to learn how to do the problem.
You are awesome @KayleeNeedsHelp ! :)

Answer 37

well thanks! I am so glad your there to help!

Answer 38

is there a way i can call you for short because its harder with your user. Thanks again, bye!

Answer 39

lol

Answer 40

you can private message me a link to your problem if that makes it easier

Answer 41

in the future if you want

Answer 42

oh yeah sure i'll message you in any case

Answer 43

but unfortunately I don't think there are any shortcuts to call people

Answer 44

XD

Answer 45

See ya later

Answer 46

see ya