# Exponential Growth or Decay

1. Dec 10, 2013

### j9mom

1. The problem statement, all variables and given/known data

State whether (e^4-x) + 2 is an exponential growth function or an exponential decay function. Explain why.

2. Relevant equations

I want to use the formula f(x) = ae^kx where a>0, and k<0.

3. The attempt at a solution

I know it is an exponential decay formula because the limit as x goes to -inf. = inf. and the limit as x goes to inf. = 2. But I do not know how to describe what a and k are in this equation to show it is an exponential decay function.

2. Dec 10, 2013

### j9mom

Ok, would I just say the parent function is f(x) = e^-1x so a is 1 and k is -1. Then the function is shifted up 2, to the left 4?

3. Dec 10, 2013

### Staff: Mentor

What you wrote is e4 - x + 2, which is a straight line whose slope is -1.

Did you mean e-4x + 2? If so, the parentheses need to be around the exponent, not the exponential expression. IOW, like this: e^(-4x) + 2.
You need parentheses here, too. f(x) = ae^(kx).

4. Dec 10, 2013

### j9mom

Yes, I did mean to type f(x) = e^(4-x) + 2

and f(x) = ae^(-kx)

Thank you for that correction

5. Dec 10, 2013

### Staff: Mentor

e4 - x = e4 * e-x = $\frac{e^4}{e^x}$