Sections 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. For example, program A may be able to complete the job in 5n 4 steps while program B might take 1.4 n steps. Which is better for a small set of data? Which is better for a large set of data?

Use the following two functions to complete the table x g(x)g(x) f(x)f(x) Which function is growing faster? Where do the two functions intersect? Use your calculator to find a window where you can see their intersection

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. x h(x) k(x)

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

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?

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 Year Population (thousands)

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?