# Exponential function help (y=ab^x)

• Apr 29th 2010, 03:40 PM
Kieth89
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.(Doh)
Any help is appreciated.
• Apr 29th 2010, 03:49 PM
skeeter
Quote:

Originally Posted by Kieth89
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.(Doh)
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 $\displaystyle a$
• Apr 29th 2010, 04:20 PM
Kieth89
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.
• Apr 29th 2010, 04:36 PM
skeeter
Quote:

Originally Posted by Kieth89
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 $\displaystyle ab = 4$ ...

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

$\displaystyle a = 6$

$\displaystyle y = ab^x$

$\displaystyle y = 6\left(\frac{2}{3}\right)^x$
• Apr 29th 2010, 05:02 PM
Kieth89
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.