Thread: 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?

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

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.

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

The exact wording of the problem is.

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

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 so

From which we can see that

So or .

Can you find

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.

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 then

Then C = 5

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.