Question

Use a graphing utility to solve each equation for $x.$ $$20=100(5)^{-x}$$

   Use a graphing utility to solve each equation for $x.$
$$20=100(5)^{-x}$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 4, Problem 56

Instant Answer

Solved by Expert Charles Carter

06/30/2020

Step 1

The first equation is a horizontal line $y=20$. The second equation is an exponential decay function $y=100(5)^{-x}$. Show more…

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Use a graphing utility to solve each equation for $x.$ $$20=100(5)^{-x}$$

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Key Concepts

Exponential Equations

An exponential equation is one in which the variable to be solved for appears in the exponent. These equations often require special methods such as taking logarithms or using numerical tools to isolate and solve for the variable, as standard algebraic techniques may not suffice.

Graphing Utilities

Graphing utilities are technological tools or software that enable users to plot equations and visually determine solutions by finding points of intersection. They provide a powerful means to approximate solutions to equations, especially when an algebraic solution is complex or difficult to obtain.

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions and are often used to solve exponential equations analytically. By taking the logarithm of both sides of an exponential equation, the variable in the exponent can be brought down and isolated, thereby converting the equation into a linear form that is easier to solve.

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