Chapter 7, Problem 73CR

To determine

To find: Whether the function $f(x)=7{\left(0.32\right)}^x$ represents exponential growth or exponential decay and identify the growth or decay factor.

Answer to Problem 73CR

The given function $f(x)=7{\left(0.32\right)}^x$ represents exponential growth with decay factor $b=0.32$ .

Explanation of Solution

Given information:

Given function $f(x)=7{\left(0.32\right)}^x$

The exponential function $y=a{\left(b\right)}^x$ when $a>0$ ,

  $(i)$ if $0<b<1$ then the function represents exponential decay with decay factor $b$

  $(ii)$ if $b>1$ then the function represents exponential growth with growth factor $b$ .

Now compare the given function $f(x)=7{\left(0.32\right)}^x$ with $y=a{\left(b\right)}^x$ , we get $a=7>0$ and $b=0.32<1$

Hence, the given function $f(x)=7{\left(0.32\right)}^x$ represents exponential decay with decay factor $b=0.32$ .