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anonymous
 5 years ago
Exponential equation. Points (2,9) (0,1). My answer y=3(1/3)^x. Am I correct?
anonymous
 5 years ago
Exponential equation. Points (2,9) (0,1). My answer y=3(1/3)^x. Am I correct?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well \[3*(1/3)^{2} = 3*3^2 = 9*3 = 27 \ne 9\] so nope. That can't be right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmm well lets see. First I got a=9/b^2. is that correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0From the second point we have \[1 = ab^0\] Since \[b^0=1\rightarrow 1 = ab^0 = a*1 \rightarrow a = 1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Try plotting y = 2^x, y = 2^(x), etc. That may give you ideas about the base and the exponent,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh well I was taught to use the first point first to find out what a equals for the b equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Anytime you have x = 0 for an exponential equation, the y value for that point is the value of a.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Because any base raised to the 0 power equals 1.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0still no comprendo senor.....or senora. You don't use the second equation for a.......gawh I wish math was simple for fooligans like me.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok. Lets break it down. We have 2 points (2,9) and (0,1) That gives 2 equations: \[9 = ab^{2}\] and \[1 = ab^0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok. So what is \[b^0=?\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is where your throwing me off. Don't i have to use the first equation for a first?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It doesn't matter. You use whichever is easier. In this case the second equation is easier. This will become apparent when you understand what b^0 is.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay. I just want to make sure. I have a test tomorrow and if i use your tricks I don't want to get penalized.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay well to me its a different way so continue senor.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you really want we can do it your way.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no I'm open to your idea. your the smarter one here so continue.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Lets do it your way and then we'll do mine and see that we get the same thing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay sounds good to me. :0]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you familiar with this notation? \[\rightarrow\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0does that mean equals or references to the next step?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not equals. It means 'implies', 'therefore', or 'leads to'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So something like \[ A = 5\] \[ A +B = 10 \rightarrow 5 + B = 10 \rightarrow B = 5\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So using the first equation and solving for a: \[9 = ab^{2}\] \[\rightarrow 9b^2 = ab^{2}b^2\] \[\rightarrow9b^2 = ab^0 \rightarrow a = 9b^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay question time! Don't you divide by b^2? and keep 9/b^2 for the next equations a? for example: 1=(9/b^2)(b^0)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then solve for b and then plug in b for the original equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ah. No because \[b^{2} = \frac{1}{b^2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So you need to multiply by b^2 in order to get a by itself, not divide.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oooooh so thats where I missed the mark. Okay i get it so if i have a negative, instead of dividing I multiply.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Think about it this way. You want to move the b over to the other side. You know that multiplying powers of the same base you add exponents right? \[a^b * a^c = a^{(b+c)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes and when you divide you subtract.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right. So here's the million dollar question. What is \[k^0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nope. 2^4 = 16 2^3 = 8 2^2 = 4 2^1 = ? 2^0 = ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0shoot I change my mind its 1!! now wheres my money?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right. So if we have \[ab^2 = 9\] We can multiply both sides by b^2 \[a*b^2*b^{2} = 9*b^{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And we end up with \[a*b^{2+ (2)} = 9b^{2} \] Which simplifies to \[a*b^{0} = 9b^{2} \] Which simplifies to \[a*1 = 9b^{2} \] Which simplifies to \[a = 9b^{2} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now that wasn't the equation we had. We had \[ab^{2} = 9\] So instead of multiplying by b^2 we need to multiply by b^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we end up with \[a = 9b^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And we plug that into the second equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So what do you get when you plug in 9b^2 for a in the second equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0after dividing 9 from 9b^2 of course.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0b=1/3 Like I had before...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah. So now plug that in for b in either of the two equations.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then i got a=1. and a full answer of y=1(1/3)^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So now look at what happens when you plug in 1/3 for b in the second equation. Does it matter what b was?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you mean? I got the whole equation right didnt i?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes. I'm trying to show my original idea.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh okay. well no it doesn't matter what b was. So yes you were right. hahaa that all you wanted to hear wasnt it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[1=ab^0\] is our second equation from the beginning. You plug in 1/3 and you get a = 1. But does it matter what you plug in for b?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no just as long as the answer is correct. :0]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right. So you can see that for exponential equations if you are given a point (0,k). You already know that a must be k.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh okay yeah I get it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Because \[ab^0= k\rightarrow a*1 = k \rightarrow a = k\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Which means you can jump right to finding b and save some time.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so if i do it either way i will end up with the right answer. Okay i'm getting your drift here. thanks a bunch! your so patient and I feel more confident it passing my test. SO thanks it really means a lot!!
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