# Thread: Find the equation of the exponential function, am I doing it wrong?

1. ## Find the equation of the exponential function, am I doing it wrong?

If I'm doing it wrong, where am I doing it wrong?

Here is my work

f(3) = 10 ; f(9) = 40

10a^6 = 40

a^6 = 4

a = 4^(1/6)

a = 1.25992105

10 = c(1.25992105)^3

1.25992105^3 ≈ 2

10/2 = C

5 = C

f(x) = 2(4)^x

is this the correct equation?

2. ## Re: Find the equation of the exponential function, am I doing it wrong?

I know I'm doing it wrong, because when I check the answer it's way off.

3. ## Re: Find the equation of the exponential function, am I doing it wrong?

Originally Posted by wolfwood
If I'm doing it wrong, where am I doing it wrong?
Here is my work
f(3) = 10 ; f(9) = 40
10a^6 = 40

I have absolutely no idea what you are doing there.
This is a perfect example of just 'jumping' into the middle of some thought process that we have no clue about.

So start over. Post the exact original wording of the question.

4. ## Re: Find the equation of the exponential function, am I doing it wrong?

Originally Posted by Plato
I have absolutely no idea what you are doing there.
This is a perfect example of just 'jumping' into the middle of some thought process that we have no clue about.

So start over. Post the exact original wording of the question.
the f(3) = 10 and f(9) = 40 are the two points we are given to find the equation.

the 10a^6 = 40 is the equation to find what a is for y = c*a^x

5. ## Re: Find the equation of the exponential function, am I doing it wrong?

The exact wording of the problem is.

Find the equation of the exponential function with f(3) = 10 and f(9) = 40

6. ## Re: Find the equation of the exponential function, am I doing it wrong?

Originally Posted by wolfwood
The exact wording of the problem is.
Find the equation of the exponential function with f(3) = 10 and f(9) = 40

That is an oddly worded question.
So you want $\displaystyle f(x)=ca^x$ so $\displaystyle 10=ca^3~\&~40=ca^9~.$

From which we can see that $\displaystyle \frac{10}{a^3}=\frac{40}{a^9}$

So $\displaystyle a^6=4$ or $\displaystyle a=\sqrt[6]{4}$.

Can you find $\displaystyle c~?$

7. ## Re: Find the equation of the exponential function, am I doing it wrong?

If I were to plug that into the formula

f(x) = ca^x

10 = c((4^1/6)^3)

I must need to review my exponents.

Would my next step be 10 = c(4)^3/6

trying to simplify my problem.

8. ## Re: Find the equation of the exponential function, am I doing it wrong?

Originally Posted by wolfwood
If I were to plug that into the formula
f(x) = ca^x
10 = c((4^1/6)^3)
Would my next step be 10 = c(4)^3/6
So $\displaystyle 10=c\sqrt{4}$ then $\displaystyle c=~?$

Then C = 5

10. ## Re: Find the equation of the exponential function, am I doing it wrong?

I did find the correct equation. What I was doing wrong was breaking 4^1/6 down to decimal form when I should have left it as 2^1/3.