Identifying Exponential Growth or Decay in (e^4-x) + 2

[j9mom]

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.

 

[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?

 

[Mark44]

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.

 

[j9mom]

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

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

Thank you for that correction

 

[Mark44]

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