No idea what I'm getting wrong... trying to find this exponential function

[William021]

Determine an exponential function that passes through the points (-3,7), (4,1.5).

f(x)=ab^x

I substitute both points to get these:

7=ab^-3
1.5=ab^4

I solve for A in 1st equation in terms of b:

7=ab^-3

a=7/b^-3
a=7b^3

I substitute A into second equation to solve for b

1.5=7b^3b^4

1.5=7b^7

b=0.80246

Now that I have B, I plug B back into a=7b^3 to get my A value:

a=7(0.80246)^3 = 3.61716
a=3.61716

answer: f(x)=.80246(3.61726)^x

But my graph looks like this:



Doesn't go through the desired points... I've checked and rechecked the math, but obviously I am missing something.

 

[R.M.]

Looks like you switched your a & b when you wrote your equation.
You desire f(x) = ab^x, but it looks like you graphed f(x) = ba^x.

 

[skeeter]

[MATH]1.5 = ab^{4}[/MATH]————
[MATH]7 = ab^{-3}[/MATH]
divide the two equations ...

[MATH]\frac{3}{14} = b^7 \implies b = \left(\frac{3}{14}\right)^{1/7}[/MATH]
[MATH]a = 7b^3 \implies a = 7 \left(\frac{3}{14}\right)^{3/7}[/MATH]
finish it ...

 

[William021]

Thanks guys, I spotted it shortly after I made the thread, silly mistake.