Question

Use a graphing utility to solve each equation. Express your answer rounded to two decimal places.

$e^x=x^3$

Short answer

The solutions of the given equation are 1.86 and 4.54.

Step-by-step solution

Step 1. Given information.

The given equation is:

$e^x=x^3$

Step 2. Determine the solution by the graphing utility.

Plot the graphs of $y_1=e^x$ and$y_2=x^3$ on a coordinate plane. The x-coordinate of the intersection point is the solution of the given equation.

The graphs intersect each other at $x\approx 1.857$ and $x\approx 4.536$. After rounding the value to two decimal places$x\approx 1.86$ and $x\approx 4.54$.

Step 3. Conclusion.

The solutions of the given equation are 1.86 and 4.54.