Question

Which is an exponential decay function?

Answer 1

Answer:

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

Step-by-step explanation:

An exponential function of the form $f(x)=a(b)^x$  will decay if $0\:$

This implies that option A will not decay because $\frac{7}{4}\:>\:1$

Option B will not decay because $f(x)=\frac{2}{3}(\frac{4}{5})^{-x}\implies f(x)=\frac{2}{3}(\frac{5}{4})^{x}$  which implies that $b=\frac{5}{4}\:>\:1$

Option C can be rewritten to get: $f(x)=\frac{3}{2}(\frac{8}{7})^{-x}\implies f(x)=\frac{3}{2}(\frac{7}{8})^{x}$....This exponential function decays.

Option D will not decay because $-\frac{9}{2}\:$

Answer 2

Answer:

Step-by-step explanation:

An exponential function of the form   will decay if

This implies that option A will not decay because

Option B will not decay because   which implies that

Option C can be rewritten to get: ....This exponential function decays.

Option D will not decay because

Step-by-step explanation: