Question

Which is an exponential decay function?

Answer 1

Answer:

$f(x)=\frac{3}{4}(\frac{7}{4})^x$

$f(x)=\frac{3}{2}(\frac{8}{7})^{-x}$

Step-by-step explanation:

An exponential decay function is of the form:

$f(x)=ab^x$, where $0\:$.

Or $f(x)=ab^{-x}$, where $|b|\:>\:1$

The coefficient 'a' can be any non-zero real number.

$f(x)=\frac{3}{4}(\frac{7}{4})^x$ is an exponential decay function, because it meets our first definition.

$f(x)=\frac{2}{3}(\frac{4}{5})^{-x}$, is not an exponential decay function.

$f(x)=\frac{3}{2}(\frac{8}{7})^{-x}$, is an exponential decay function, because it meets our second definition.

$f(x)=\frac{1}{3}(-\frac{9}{2})^x$ is also NOT an exponential decay function.