Question

Which function represents exponential decay? f(x) = One-half (three-halves) Superscript x f(x) = One-half (negative three-halves) Superscript x f(x) = 4(negative two-thirds) Superscript x f(x) = 4(two-thirds) Superscript x

Answer 1

Answer:

$f(x) = 4(\frac{2}{3})^{x}$

Step-by-step explanation:

The first function is given as, $f(x) = \frac{1}{2}(\frac{3}{2})^{x}$.

Now, the value of this function increases i.e. value of f(x) increases as the x-value increases because $\frac{3}{2} > 1$.

Now, the second function is given as, $f(x) = \frac{1}{2}(- \frac{3}{2} )^{x}$.

This function can not be considered as a continuous function because $- \frac{3}{2} < 0$.

Again, the third function is given as, $f(x) = 4(- \frac{2}{3})^{x}$.

This function can also not be considered as a continuous function because $- \frac{2}{3} < 0$.

Finally, the fourth function is given to be, $f(x) = 4(\frac{2}{3})^{x}$.

In this function, the value of f(x) continuously decreases as the value of x increases, because $0 < \frac{2}{3} < 1$.

Therefore, this function represents exponential decay. (Answer)

Answer 2

Answer:

D

Step-by-step explanation: