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enter image description here

I am struggling to get an equation from the graph above

I know

${f(x) = ba^x + c}$

When y = 0, x = -2

${b = -2}$

${24 = -2a^3}$

${2a^3 = -24}$

${a = {\sqrt[3]{{-24}\over 2}}}$

dagda1
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    please explain why this is marked down. – dagda1 Jan 07 '16 at 21:06
  • Were you asked to use the model $f(x)=ba^x+c$? Because in that model there are three unknown parameters (b, a, and c). In which case you would need three points to determine the equation, but you only are given two. Are you maybe supposed to just use $f(x)=ba^x$? In that case you are on the right track, though I think you made a typo. Do you mean when $x=0$, $y=-2$ to conclude that $b=-2$? – wgrenard Jan 07 '16 at 21:48
  • i was not asked but people on this site are very rude when it comes to people who are just starting out. I have never tried to write the equation of an exponential graph in my life so I used google and came across the for ba^x + c You did not even explain why you marked me down. If the question annoys you then why not ignore it? – dagda1 Jan 07 '16 at 22:23
  • I'm not the one that voted the question down. I actually voted the question back up because I don't feel like it should have been downvoted. – wgrenard Jan 07 '16 at 22:25
  • Is it possible to assume that when x=2, y=0 (using the graph)? – NoChance Jan 07 '16 at 22:28
  • Yea, working off of NoChance's comment, are you given any information on what the x-intercept is? – wgrenard Jan 07 '16 at 22:30
  • I have got this answer assuming that y=0 at x=2. If you are interested I can write down the steps. $$y=-13(-1^{x})+11$$. – NoChance Jan 07 '16 at 22:51

1 Answers1

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There are different models that you can use to express exponential functions. A common one is:

$$y = ba^x$$

Though you can also use the model $y = ba^x + c$ as you have proposed, this model includes three unknown parameters. Thus, to find an equation fitting this model, you would need to be given three points. However, you are only given two points, so this model will not work here.

So, assuming we want to use the common model I mentioned above, we note that on the given curve when $x=0$, $y=-2$. Plugging these values into the formula we find that $b=-2$.

Using this result, you have already shown that you can then figure out

$$a=\sqrt[3]{\frac{-24}{2}}$$

Note, however, that this is not the simplest form, so you should simplify it. Now, all that remains is to plug the parameters $b$ and $a$, which you now know, back into the general formula $y=ba^x$.

As you can see, you have done most of the work to get to the correct answer, but I hope I've cleared up some confusion on the process of getting the correct result.

wgrenard
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