Mathematics

Problem

Let

g(x)=b^{x}

where

0<b<1

. Answer the following. a. (i) Show that

g(x)

is a decreasing function on

\mathbb R

. b. (ii) Solve the inequality

0.4^{2x-3}>0.4^{x+1}

for real

x

, giving the solution set in interval notation. c. (iii) Using your answer to part (ii), determine which number is larger:

A=0.4^{\sqrt{5}}

B=0.4^{\sqrt{7}-1}

. Give reasons for your choice.