# Exponential Growth or Decay

## Homework Statement

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

## Homework Equations

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

## 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.

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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?

Mark44
Mentor

## Homework Statement

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

## Homework Equations

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

## 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.

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

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

Thank you for that correction

Mark44
Mentor
e4 - x = e4 * e-x = ##\frac{e^4}{e^x}##

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