Q. 57 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $57-64$, use a graphing utility to solve each system of equations. Express the solution(s) rounded to two decimal places.

$\left\{\begin{array}{l}y=x^{\frac{2}{3}}\\ y=e^{-x}\end{array}\right.$

Step-by-Step Solution

Answer

The graph for the equation $\left\{\begin{array}{l}y=x^{\frac{2}{3}}\\ y=e^{-x}\end{array}\right.$ is,

From the graph, the intersecting point is, $\left(0.48,0.62\right)$.

Step 1. Given information

$\left\{\begin{array}{l}y=x^{\frac{2}{3}}\\ y=e^{-x}\end{array}\right.$

Now draw a graph for the given equation.

Step 2 Now observe the graph.

In the graph, the given equations are intersecting at the point $\left(0.48,0.62\right)$.

So, the given system has only one solution.