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Homework Help: Exponential Growth or Decay

  1. Dec 10, 2013 #1
    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. jcsd
  3. Dec 10, 2013 #2
    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?
  4. Dec 10, 2013 #3


    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).
  5. Dec 10, 2013 #4
    Yes, I did mean to type f(x) = e^(4-x) + 2

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

    Thank you for that correction
  6. Dec 10, 2013 #5


    Staff: Mentor

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