Question

Hi!
I have to put down this formula y = ab^x and I need help with it.

Answer 1

Yes you are. Next, I would divide the second equation by the first equation.

Answer 2

so 4 by 16 or the whole things?

Answer 3

IN order to maintain equality you have to divide both sides. Like this:\[\frac{ 16 }{ 4 } = \frac{ ab^{-3} }{ ab^{-1} }\]

Answer 4

so b = 4 then

Answer 5

Well, carrying out the division above, you'll get\[4 = b^{-2} = \frac{1}{b^2}\]Can you solve for b?

Answer 6

um sorry I don't know what exactly to do... i'm trying to think

Answer 7

Let's back up a bit and make sure you're OK with the division.

Answer 8

1/2

Answer 9

You had\[\frac{ 16 }{ 4 } = \frac{ ab^{-3} }{ ab^{-1} }\]The left hand side is easy. On the right hand side, the a's will cancel out, leaving\[4=\frac{ b^{-3} }{ b^{-1} }\]Are you OK with it so far?

Answer 10

You are correct, b = 1/2

Answer 11

oh okay yeah I see duh lol

Answer 12

You're doing a good job. Now, substitute b=1/2 into either of the given equations and solve for a.

Answer 13

The first one might be easier to work with\[4=a \left( \frac{ 1 }{ 2 } \right)^{-1}\]

Answer 14

okay um 2?

Answer 15

Correct. Well done.

Answer 16

how would the second equation be set up? same thing just replace the 4?

Answer 17

Well, you don't really need it. You already have the answer, but if you chose to work with the second equation instead, it would look like\[16 = a \left( \frac{ 1 }{ 2 } \right)^{-3}\]and you get the same answer, a=2.

Answer 18

or don't we have to do 16/4?

Answer 19

oh okay

Answer 20

okay so what's next?

Answer 21

You need one more step: reject the value b =-1/2
Since \(b^2=\dfrac{1}{4}\\b=\pm\sqrt{\dfrac{1}{4}}=\pm\dfrac{1}{2}\)

Answer 22

You have a and b. Put them into the general function\[y=ab^x\]What do you get?

Answer 23

y= 2(1/2)^x ?

Answer 24

Excellent. Well done.

Answer 25

or y= 2(0.5)^x

Answer 26

Whichever you teacher (or courseware) prefers.

Answer 27

I think he wants decimal. Anyways merci beaucoup! I appreciate this so much. You rock

Answer 28

You're welcome