Lesson 7
1. Lesson 7
1.5. Explore
Module 7: Exponents and Logarithms
Explore
In Try This 1, you may have discovered that the model that would best fit the cooling cup of coffee is the exponential regression equation y = 82.63(0.956)x. This is the form of exponential equation you saw in Lesson 1 (y = abx, b > 0, b ≠ 1). The data points lie close to this function; therefore, it is a good model for the data.
Adapted from Stockbyte/Thinkstock
Read “Example 1” on pages 371 to 373 of your textbook to see how an exponential regression can be used to make predictions using interpolation and extrapolation. In this problem, time is inputted as 10-year increments instead of using the years listed in the table. Typically, when years (such as 1871 or 1992) are used when performing a regression, the resulting equation is very sensitive to rounding. To avoid this, the number of years past a time is often used for regressions. In this example, 10-year increments are used.
Read and note the section titled “Key Idea” on the bottom of page 376. This provides a summary of exponential regression.