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Chapter 3: Problem 48

Use a graphing utility to graph the exponential function. $$s(t)=3 e^{-0.2 t}$$

Short Answer

Expert verified
The function \(s(t)=3 e^{-0.2 t}\) graphs an exponential decay. The graph begins at \(y=3\) when \(t=0\) and decreases towards the x-axis (without crossing it) as \(t\) increases.

Step by step solution

01

Understand the given function

This function is an exponential decay function and it is in the form of \(s(t)= a e^{-kt}\), where \(a=3\) and \(k=0.2\). The values of \(a\) and \(k\) would dictate how the graph appears. In this case, the number 3 suggests that the graph is shifted upward by 3 units from the usual location of an exponential graph. The exponent \(-0.2t\) indicates that the function decreases as \(t\) increases, suggesting an exponential decay.
02

Use a Graphing Utility

Choose a graphing tool such as a graphing calculator or software. Next, you input the function \(s(t)=3 e^{-0.2 t}\) into the graphing utility. You will then see the output of the function as \(t\) varies. You should do this for a range of \(t\) which typically should be from \(-10 \leq t \leq 10\) or based on the specific requirements of the exercise.
03

Interpret the Graph

Once you input the function and generate the graph, you should identify key features of the graph. You'll notice it is a curve that begins at \(y=3\) when \(t=0\) and steadily decreases towards the x-axis (without touching it) as \(t\) increases. Because of the negative exponential, the graph will show an exponential decay.

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