Answer:
[tex]f(x)=\frac{3}{2}(\frac{8}{7})^{-x}[/tex]
Step-by-step explanation:
An exponential function of the form [tex]f(x)=a(b)^x[/tex] will decay if [tex]0\:<\:b\:<\:1[/tex]
This implies that option A will not decay because [tex]\frac{7}{4}\:>\:1[/tex]
Option B will not decay because [tex]f(x)=\frac{2}{3}(\frac{4}{5})^{-x}\implies f(x)=\frac{2}{3}(\frac{5}{4})^{x}[/tex] which implies that [tex]b=\frac{5}{4}\:>\:1[/tex]
Option C can be rewritten to get: [tex]f(x)=\frac{3}{2}(\frac{8}{7})^{-x}\implies f(x)=\frac{3}{2}(\frac{7}{8})^{x}[/tex]....This exponential function decays.
Option D will not decay because [tex]-\frac{9}{2}\:<\:0[/tex]
