Chapter 6.4, Problem 2Q

To determine

To check: Whether the function $y={\left(\frac{3}{8}\right)}^x$ represents exponential growth or decay.

Answer to Problem 2Q

The function $y={\left(\frac{3}{8}\right)}^x$ represents exponential decay.

Explanation of Solution

Given information:

The function is $y={\left(\frac{3}{8}\right)}^x$ .

Calculation:

An exponential function has a form of $y=a{b}^x$ . Here, the growth factor is $b$ and the value of $a\ne 0$ .

An exponential function is said to be an exponential growth function if it has a form of $y=a{b}^x$ where $a>0$ and $b>1$ .

An exponential function is said to be an exponential decay function if it has a form of $y=a{b}^x$ where $a>0$ and $0<b<1$ .

Compare the given function with standard form of exponential function.

  $a=1$ , $b=\frac{3}{8}\approx 0.375$

From the above, it is clear that the value of $a\ne 0$ and $b<1$ .

Therefore, the function $y={\left(\frac{3}{8}\right)}^x$ represents exponential decay.