Learning Resources
Lesson
Using the ideas that you have learned in this section you should now be able to write functions to model the bacteria growth in the hamburger meat prepared by Richard, John, and Sadie. You can then use these equations and your TI 83 to sketch the graphs of the corresponding functions.
Start with the exponential equation:
Then use the information about each lot of hamburger meat to determine the value of a, b, and c for each of the functions. (Do you recall what a, b, and c in the equation represent about the original data? If not go back and look at the examples in Lesson 03 in this Section.)
Be careful in trying to write a function for the bacteria in the meat that Sadie brings. It is a bit more difficult since you will have to consider three different situations:
- the first 2 hours when the doubling time was 15min;
- the next 20.5 hours when it was frozen and there was no growth;
- the remaining 2.5 hours when the doubling time was 45 min.
This gives rise to what is referred to as a piecewise function since the resulting graph will have three distinct pieces to it to match each of the time periods.
You should discuss your solution to this part of the Chapter Project with your classmates and your on-line teacher.
Activity
- Refer to the directions on page 142 and complete parts (a) and (b) of the Chapter Project on pages 124 & 125.
Test Yourself
There are no extra questions for this lesson. Simply submit your work to date to your online teacher.