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Chapter 3: Problem 65

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$8 e^{-2 x / 3}=11$$

Short Answer

Expert verified
The approximate value of \(x\) for which \(8 e^{-2x / 3}=11\) can be found by graphing the equation and approximating the x-intercept. The obtained value of \(x\) should ensure that the LHS of the equation approximately equals 11 when substituted back into the equation.

Step by step solution

01

Graph the Equation

Start by graphing the equation \(8 e^{-2 x / 3}=11\) using a graphing utility like Desmos or Grapher. The graph will intersect the x-axis at the solution of the equation.
02

Approximate the Solution

The solution of the equation is the x-coordinate of the point where the graph intersects the x-axis. Use the zoom and trace features of the graphing utility to approximate this value to 3 decimal places.
03

Verification of the result

Substitute the obtained value of \(x\) into the original equation to verify the result. The left-hand side (LHS) of the equation should approximately equal the right-hand side (RHS) of the equation, i.e., 11.

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