SOLUTION: Not sure if this is in the right section, but hoping for some help. I have this question on my practice sheet for a final coming up, it says... Suppose that f(x) is exponential

Algebra ->  Functions -> SOLUTION: Not sure if this is in the right section, but hoping for some help. I have this question on my practice sheet for a final coming up, it says... Suppose that f(x) is exponential      Log On


   

Question 379554: Not sure if this is in the right section, but hoping for some help. I have this question on my practice sheet for a final coming up, it says...
Suppose that f(x) is exponential and that f(-3)=54 and f(2)=2/9. Find a formula for f(x).
I don't even know what this means!! It says it's exponential, does that mean it's an exponential function and I should assume f(x)=ab^x? Isn't that a formula itself? I'm not sure what to do here or how to even start on this. Is my math teacher just wording this poorly or am I lost? Help! :)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, an exponential function has the form, y=ab%5Ex
Use both points.
f%28-3%29=54
1.54=ab%5E%28-3%29
.
.
f%282%29=2%2F9
2.2%2F9=ab%5E%282%29
.
.
.
Divide eq. 2 by eq. 1 to eliminate a.
.
.
%282%2F9%29%2F54=%28ab%5E2%29%2F%28ab%5E%28-3%29%29
b%5E5=1%2F243
highlight%28b=1%2F3%29
.
.
Then use either equation to solve for a.
2%2F9=a%281%2F3%29%5E2
2%2F9=a%2F9
highlight%28a=2%29
.
.
highlight_green%28y=2%281%2F3%29%5Ex%29