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Chapter 3: Problem 45

Use a graphing utility to graph the exponential function. $$y=1.08 e^{-5 x}$$

Short Answer

Expert verified
The graph of the function \(y=1.08e^{-5x}\) starts at the y-intercept (0, 1.08) and decreases towards the x-axis as \(x\) increases, indicating that this is an exponential decay function.

Step by step solution

01

Understand Function Basics

First, analyse the given exponential function \(y=1.08e^{-5x}\), where \(e\) is the base of natural logarithms, and -5 is the coefficient of \(x\). This function models exponential decay because -5 is a negative number.
02

Find the y-Intercept

The y-intercept is the output of the function when \(x=0\). Substituting \(x=0\) into the function yields \(y=1.08e^{0} = 1.08\). So, the y-intercept is at the point (0, 1.08).
03

Use a Graphing Utility

Use an appropriate graphing tool or calculator and input the function \(y=1.08e^{-5x}\). Trace the curve to analyze its shape and nature. The curve will start at the y-intercept and decrease towards the x-axis as \(x\) increases.

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