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Thread: Exponential function help (y=ab^x)

  1. #1
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    Exponential function help (y=ab^x)

    I need help finishing this problem. I need to write an exponential function of the form $\displaystyle y=ab^x$whose graph passes through the given points. The points are (1,4) and (2, 8/3), the 8/3 is a fraction. I find a in the last set of points, and then use that to substitute for a in the top set, but after that I can't figure out how to simplify and find b. I know it has something to do with logs.
    Any help is appreciated.
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  2. #2
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    Quote Originally Posted by Kieth89 View Post
    I need help finishing this problem. I need to write an exponential function of the form $\displaystyle y=ab^x$whose graph passes through the given points. The points are (1,4) and (2, 8/3), the 8/3 is a fraction. I find a in the last set of points, and then use that to substitute for a in the top set, but after that I can't figure out how to simplify and find b. I know it has something to do with logs.
    Any help is appreciated.
    $\displaystyle 4 = ab^1 = ab$

    $\displaystyle \frac{8}{3} = ab^2 = ab \cdot b = 4b$

    solve for $\displaystyle b$ , then find $\displaystyle a$
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    I understand what you did skeeter. I can get that far on my own. I get all this:

    2=ab^(8/3)
    $\displaystyle 4=ab^ 1$
    so
    a=2/b^(8/3)

    substitute:
    4=(2/b^(8/3) )*b

    $\displaystyle 2=b^5/3$

    Now I *think* that logs come into play, but I don't know how or what to do to get b. That's what I can't figure out.

    I don't know how to get the forums to register that 8/3 is a fraction exponent, so I couldn't put those in the math looking font thingy. Sorry.
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    Quote Originally Posted by Kieth89 View Post
    I understand what you did skeeter. I can get that far on my own. I get all this:

    2=ab^(8/3)
    $\displaystyle 4=ab^ 1$
    so
    a=2/b^(8/3)

    substitute:
    4=(2/b^(8/3) )*b

    $\displaystyle 2=b^5/3$

    Now I *think* that logs come into play, but I don't know how or what to do to get b. That's what I can't figure out.

    I don't know how to get the forums to register that 8/3 is a fraction exponent, so I couldn't put those in the math looking font thingy. Sorry.
    why are you making $\displaystyle \frac{8}{3}$ an exponent ? it's a y-value.

    $\displaystyle 4b = \frac{8}{3}$

    $\displaystyle b = \frac{8}{12} = \frac{2}{3}$

    since $\displaystyle ab = 4$ ...

    $\displaystyle a \cdot \frac{2}{3} = 4$

    $\displaystyle a = 6$


    $\displaystyle y = ab^x$

    $\displaystyle y = 6\left(\frac{2}{3}\right)^x$
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    Ooooooooooooppps....I think I should read each problem twice from now on, somehow I got the x and y switched around and never noticed. Even though I have re-typed this problem numerous times tonight.
    That makes the problem a lot simpler. Thanks for the help. I'll be sure to remember to read each question twice on my test tomorrow.
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