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Chapter 3: Problem 31

Use a graphing utility to graph the exponential function. $$y=3^{x-2}+1$$

Short Answer

Expert verified
You should obtain a graph for the function \(y=3^{x-2}+1\), shifted 2 units to the right and 1 unit upwards compared to the standard \(y=3^x\) graph.

Step by step solution

01

Understand the Function

Recognize that \(y=3^{x-2}+1\) is an exponential function, where 3 is the base and the function has a 'shift' due to the '-2' and '+1' in the equation. The '-2' shifts the graph 2 units to the right, and the '+1' shifts it 1 unit upwards.
02

Choose a Graphing Utility

Choose a graphing utility that you are comfortable with to draw this function. There are many graphing calculators available online. Some of these include GeoGebra, Desmos, and GraphFree.
03

Input Function

Enter the function \(y=3^{x-2}+1\) into the graphing utility. Most tools will have a specific area for you to input this function
04

Generate and Analyze the Graph

Usually, the utility will generate the graph automatically once you input the function. If it doesn't, there will likely be a 'Graph' or 'Enter' button that you can press. Look at the graph and confirm that it meets the characteristics of your function, such as moving 2 units to the right and 1 unit upwards.

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Most popular questions from this chapter

If $$\$ 1$$ is invested in an account over a 10-year period, the amount in the account, where \(t\) represents the time in years, is given by \(A=1+0.075 \llbracket t \rrbracket\) or \(A=e^{0.07 t}\) depending on whether the account pays simple interest at \(7 \frac{1}{2} \%\) or continuous compound interest at \(7 \%\). Graph each function on the same set of axes. Which grows at a higher rate? (Remember that \(\llbracket t \rrbracket\) is the greatest integer function discussed in Section 1.6.)

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Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. $$2 x \ln x+x=0$$

The sales \(S\) (in thousands of units) of a new CD burner after it has been on the market for \(t\) years are modeled by \(S(t)=100\left(1-e^{k t}\right) .\) Fifteen thousand units of the new product were sold the first year. (a) Complete the model by solving for \(k\). (b) Sketch the graph of the model. (c) Use the model to estimate the number of units sold after 5 years.

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x+\ln (x-2)=1$$
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