# Example of an exponential model

EXPONENTIAL MODELING:

I want you to locate data that can be effectively modeled using an exponential function. Check the scatter plot to be sure that your data is appropriate for an exponential model! Please include the following components in your finished assignment:

1. A data table showing your original data, with a reference to the original source of the data. The reference should be reproducible (i.e. if I were to go to the same source, I would find the data.)

2. A brief discussion telling why you chose this particular data set to study. As in discussion two, I am hoping that you will choose data that has some relevance to your life. It may be related to an interest of yours, your job, your future career goal, etc.

3. Use exponential regression on your calculator to find the equation of an exponential model for your data.

4. Use the model to draw some type of conclusion. You may want to predict something about the future. You may also want to make some comments about the range of validity of your model (i.e. when does model breakdown occur?).

5. Discuss the base, b, of your model and tell what it means in real-world terms.

Once again, if you have trouble finding data you may wish to make use of the textbook website: www.prenhall.com/lehmann.

If you go to Chapter 4 "Exponential Functions", and select "data links" from the menu on the left, you will get a large number of links to data. Again, caution!!!! Not all of the data you will find at these sites is exponential. Make a good choice of data sets on which to base your assignment.

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#### Solution Preview

EXPONENTIAL MODELING:

I want you to locate data that can be effectively modeled using an exponential function. Check the scatter plot to be sure that your data is appropriate for an exponential model! Please include the following components in your finished assignment:

1. A data table showing your original data, with a reference to the original source of the data. The reference should be reproducible (i.e. if I were to go to the same source, I would find the data.)

2. A brief discussion telling why you chose this particular data set to study. As in discussion two, I am hoping that you will choose data that has some relevance to your life. It may be related to an interest of yours, your job, your future career goal, etc.

3. Use exponential regression on your calculator to find the equation of an exponential model for your data.

4. Use the model to draw some type of conclusion. You may want to predict something about the future. You may also want to make some comments about the range of validity of your model (i.e. when does model breakdown occur?).

5. Discuss the base, b, of your model and tell what it means in real-world terms.

Once again, if you have trouble finding data you may wish to make use of the ...

#### Solution Summary

The solution consists of a real-life data set that can be modeled by an exponential function, the function that best models the data, and a discussion of the model and the breakdown of the model

Expotential functions and logarithmic functions

1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case.

2. Assume that the number of viruses present in a sample is modeled by the exponential function "f(t) = 10t," where t is the elapsed time in minutes. How would you apply logarithms to determine when the sample will grow to 5 billion viruses?

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