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Montano1993 [528]
1 year ago
13

Identify whether the equation represents an exponential growth or exponential decay function.1. y = 1/4 (1/e)^-2x2. y = (1/e)^4x

3. y = 2e^-x + 1How do you do this?
Mathematics
1 answer:
zvonat [6]1 year ago
5 0

The general formula for exponential growth and decays is:

y=y_0e^{kx}

if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.

Now we need to classify each of the functions:

1.

The function

y=\frac{1}{4}(\frac{1}{e})^{-2x}

can be wrtten as:

\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}

comparing with the general formula we notice that k=2, therefore this is an exponential growth.

2.

The function

y=(\frac{1}{e})^{4x}

can be written as:

\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}

comparing with the general formula we notice that k=-4, therefore this is an exponential decay.

3.

The function

y=2e^{-x}+1

comparing with the general formula we notice that k=-1, therefore this is an exponential decay.

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