Question

Does the function f(x) = 25e-2x represent exponential growth, decay, or neither?

Answer 1

The given function f(x) = 25e^(-2x) represent the exponential decay.

According to th egiven question.

We have an exponential function.

f(x) = 25e^(-2x)

As we know that

If $P = P_{o} e^{-kt}$ be an exponential function, then it will represent

• an exponential growth if  0 < e^(-k) < 1
• an exponential decay if e^(-k) >1

Where,

P is the final amount

$P_{o}$ is the intial amount

t is the time interval

k is the constant of proportionality

For the given question if we compare the given exponential function with the standard exponentential function we get

$P_{o}$ = 25

k = 2

and t = x

Now,

e^(-2) = 0.13

Since, e^(-2) < 1.

Hence, the given function f(x) = 25e^(-2x) represent the exponential decay.

Find out more informationa about exponential decay and exponential growth here:

brainly.com/question/14355665

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