Answer:
[tex]f(x)=\frac{3}{4}(\frac{7}{4})^x[/tex]
[tex]f(x)=\frac{3}{2}(\frac{8}{7})^{-x}[/tex]
Step-by-step explanation:
An exponential decay function is of the form:
[tex]f(x)=ab^x[/tex], where [tex]0\:<\:b\:<\:1[/tex].
Or [tex]f(x)=ab^{-x}[/tex], where [tex]|b|\:>\:1[/tex]
The coefficient 'a' can be any non-zero real number.
[tex]f(x)=\frac{3}{4}(\frac{7}{4})^x[/tex] is an exponential decay function, because it meets our first definition.
[tex]f(x)=\frac{2}{3}(\frac{4}{5})^{-x}[/tex], is not an exponential decay function.
[tex]f(x)=\frac{3}{2}(\frac{8}{7})^{-x}[/tex], is an exponential decay function, because it meets our second definition.
[tex]f(x)=\frac{1}{3}(-\frac{9}{2})^x[/tex] is also NOT an exponential decay function.
