Chapter 3, Problem 1PS

To determine

To find: the curves intersects the line $y=x$ , and to find all positive numbers $y=x$ for which the curve $y=a^x$ intersects the line $y=x$ .

Answer to Problem 1PS

“Hence, we can observe from the graph that the line $y=x$ intersects curves $y={0.5}^x$ and $y={1.2}^x$ .

Explanation of Solution

Given information:

The exponential function $y=a^x$ for $a=0.5,1.2$ and 2.0

Calculation:

Let us draw the graph of $y=a^x$ for $a=0.5,1.2$ and 2.0

  

Let us also draw the graph of $y=a^x$ for $a=0.5,1.2$ and 2.0 and of $y=x$

  

“Hence, we can observe from the graph that the line $y=x$ intersects curves $y={0.5}^x$ and $y={1.2}^x$ .