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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 graph of the function \(s(t)=3 e^{-0.2 t}\) is a decreasing curve, demonstrating the typical characteristic of a decaying exponential function due to the negative exponent.

Step by step solution

01

Identify the type of function

Firstly, the function \(s(t)=3 e^{-0.2 t}\) is an exponential function. Exponential functions have the form \(f(x)=ab^x\), where a and b are constants, b is positive and b is not equal to 1.
02

Understand the specific coefficients and variables of the function

In the function \(s(t)=3 e^{-0.2 t}\), the number 3 would be identified as 'a', the base is the fixed number 'e' (approximately equal to 2.71828), and -0.2t represents 'x'. Here, 'e' to the power of -0.2t causes the function to decrease as t increases, which will be seen in the graph.
03

Use the graphing utility

For this step, place the function into a graphing utility. This may be found online or on a calculator, if present. It can usually be done by inputting the function as it is presented: \(s(t)=3 e^{-0.2 t}\). Most utilities will immediately plot the function upon input.
04

Understand the graph

Finally, observe the graph created by the utility. It should show the value of the function decreasing as time (\(t\)) increases, as expected with a negative exponent. This is a typical characteristic of decaying exponential functions.

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