In Problems 57-64, use a graphing utility to solve each...

In Problems $57-64$, use a graphing utility to solve each system of equations. Express the solution(s) rounded to two decimal places.
$$
\left\{\begin{array}{l}
y=x^{2 / 3} \\
y=e^{-x}
\end{array}\right.
$$

Key Concepts

Power Function

A power function is defined by an expression where the variable is raised to a constant exponent, such as y = x^(n), where n is any real number. These functions can exhibit diverse behaviors including polynomial growth or decay, and when the exponent is fractional, they may produce graphs with unique features like cusps or non-standard symmetry.

Graphing Utility

A graphing utility is a tool, typically software-based, that allows users to visually display mathematical equations on a coordinate plane. It is especially useful for solving systems of equations by providing graphical representations of the functions, enabling users to identify points of intersection and analyze the behavior of each function.

System of Equations

A system of equations consists of two or more equations that are solved together since they share common variables. The aim is to find the values of these variables that satisfy every equation in the system simultaneously, which can often be represented as points of intersection between the graphs of each individual equation.

Intersection Points

Intersection points are the coordinates where two or more graphs cross or meet. In the context of solving systems of equations, these points represent the solutions that satisfy all the equations in the system simultaneously. Graphical methods are particularly useful for approximating these points, especially when an algebraic solution may be difficult to find.

Exponential Function

An exponential function features a constant base raised to a variable exponent, typically represented as y = a^x, though modifications like y = e^(-x) adjust its behavior. Exponential functions are characterized by rapid rates of growth or decay, and their graphical properties make them important in modeling a wide variety of real-world phenomena.

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