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Sections 9.6 + 9.7 Power, Exponential, Log, and Polynomial Functions

Sections 9.6 + 9.7 Power, Exponential, Log, and Polynomial Functions. In computer science, the number of operations required for a program to solve a problem is often stated as a function of the size of the input data set.

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Sections 9.6 + 9.7 Power, Exponential, Log, and Polynomial Functions

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  1. Sections 9.6 + 9.7Power, Exponential, Log, and Polynomial Functions

  2. In computer science, the number of operations required for a program to solve a problem is often stated as a function of the size of the input data set. • For example, program A may be able to complete the job in 5n4 steps while program B might take 1.4n steps. • Which is better for a small set of data? • Which is better for a large set of data?

  3. Use the following two functions to complete the table • Which function is growing faster? • Where do the two functions intersect? • Use your calculator to find a window where you can see their intersection

  4. Now use the following functions to complete the table • Which function is growing faster? • Where do they intersect? • Use your graphing calculator to find out.

  5. We have now encountered three basic families of functions • Linear • Power • Exponential • We can find a unique function for each given two points • Let’s find one of each that go through the points (-1, ¾) and (2, 48) • Let’s take a look at their graphs • Use a window of -3 ≤ x ≤ 3 and -10 ≤ y ≤ 50

  6. Modeling Data • Think way back to chapter 3 we used exponential functions to model quantities that were both growing and decaying • Why would we like to be able to find a function that models a given data set?

  7. The following table contains the population of the Houston-Galveston-Brazonia metro area • Create a scatter plot of the data (use t = 0 to represent the year 1900) • What type of shape does the data have? • Use your calculator to fit an exponential function to the data • Use your calculator to fit a power function to the data

  8. Graph your two functions together with your scatter plot • Use each model to predict the population in 1975 and 2010 • What do you think about your answers? • What do you think about predicting the population in 2050?

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