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?

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.

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

Quote:

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.

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

Quote:

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

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

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

Quote:

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 $\displaystyle c~?$

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.

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

Quote:

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 $\displaystyle c=~?$

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

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.