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Chapter 3: Problem 64

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$6 e^{1-x}=25$$

Short Answer

Expert verified
The approximate solution to the equation \(6e^{1-x} = 25\) is \(x = 0.471\).

Step by step solution

01

Graph the Equation

First, input the equation \(6e^{1-x}=25\) into a graphing utility, and graph it. The x-intercept of this graph will give the solution to the equation, as that is the point where the graph crosses the x-axis, or in other words, where the equation equals zero.
02

Approximate the Solution

The graph shows the function crossing the x-axis at approximately \(x=0.471\). This is the approximate solution to the equation.
03

Verify the Solution Algebraically

Next, verify the solution by substituting \(x=0.471\) into the original equation and calculating the resulting value. If the left and right sides of the equation are approximately equal, then the solution is verified. Solve for \(6e^{1-x} = 6e^{1-0.471}\) using a calculator to get approximately 25. This verifies the result.

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