Chapter 9.9, Problem 34HP

To determine

To calculate: To graph two equations in the first quadrant on the same coordinate plane and explain which graph shows faster growth.

Answer to Problem 34HP

Thegraph of $y=x^3$ shows faster growth

Explanation of Solution

Given information: Equations are $y=x^2$ and $y=x^3$

Calculation:

Equations are given as

  $y=x^2$

  $y=x^3$

In order to plot the graph of equations, find solutions of each

When $x=0$

  $\begin{array}{l}y=0^2=0\\ y=0^3=0\end{array}$

When $x=1$

  $\begin{array}{l}y=1^2=1\\ y=1^3=1\end{array}$

When $x=2$

  $\begin{array}{l}y=2^2=4\\ y=2^3=8\end{array}$

When $x=3$

  $\begin{array}{l}y=3^2=9\\ y=3^3=27\end{array}$

Now plotting the graph of the function on same coordinate plane

  

The graph of $y=x^3$ shows faster growth

Conclusion:

Hence, graph of $y=x^3$ shows faster growth