Welcome back, students. This semester we have two big goals: preparation for the GHSGT and completion of the Math III curriculum.
January 4-January 20 (updated for snow delay) Continue solving equations using exponential and logarithmic functions and extend these concepts to inequalities. Generate the exponential or logarithmic models that match given points (similar to finding the a, b, and c of a quadratic function given three points, a process we used first semester). Solve a variety of equations using all the models from this course.
Homework January 4: FInish any problems from the diagnostic test that you were not able to complete in class. Turn in on Wednesday.
Homework January 5: From the textbook, p 161 problem 41. Show how you worked the problem. ALSO page 162, your choice of 10, showing all work.
Homework January 6th: Finish the yellow sheet (side 12.8 only). For problems 7 and 8, the wording ofthe problems should be interpreted as annual "compounding." For instance, use 250,000*(1-.12)^t=100,000 for problem 7.
The other handout (6 sides/3 pages) provides another explanation of the steps for solving all these types of problems and a handful of problems of each type. PLEASE NOTE: Maddy B detected an error in the first example on the first page. See if you can find the error and, of course, do not work problems that way! Make sure you are proficient in solving these problems independently.
Homework January 7th: Pages 187&188 in the note-taking guide (the two-sided page handed out in class today) AND the exponential growth and decay problem worksheet handed out. Prepare for the test by working these problems. You can check out the websites linked below for self-quizzes and examples.
GEORGIA HIGH SCHOOL TEST ITEMS!!! Click here for the PDF file of released test items.
Test on Exponential and logarithmic applications and inequalities on Thursday, Jan 20th.(Delayed one week because of snow days)
Cool websites for review of logarithms and exponential functions:
http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/log_exp/logandexponentialquizsoln.html
http://wps.prenhall.com/esm_goldstein_calculus_10/9/2374/607804.cw/index.html
http://www.mathwarehouse.com/exponential-growth/exponential-models-in-real-world.php
http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/log_exp/realworldappsexponential.html
http://quiz.econ.usyd.edu.au/mathquiz/logarithms/quiz2.php
http://quiz.econ.usyd.edu.au/mathquiz/logarithms/quiz3.php
Math III Log and Exponential Inequalities and Applications Test Study Guide
To be successful, you must be able to
Interpret the different parts of the formula for exponential growth or decay, for instance, the growth rate, the initial amount, the final amount, the growth factor.
Use formulas for growth and decay and formulas using logarithms to solve real-world word problems. You have to be efficient with these! This will be the largest part of the test.
Apply the principles and procedures of exponential and logarithmic functions to solve equations and inequalities. Express the solutions to inequalities in both graphical and interval form (both graphing on a number line and the interval notation with parentheses, brackets, and upper and lower bounds).
FAQ
I'm trying to work some exponential problems that do not involve interest. How will I know if the problem uses continuous "compounding" or annual "compounding"?
Scenarios such as population growth and bacteria colonies grow continuously, so your model should be based on Pert, the continuous growth model. On the other hand, if the problem involves something that increases only once per period, use the model that looks like annual compounding. It is possible to justify either approach for many problems. Can you support your choice based on the language of the problem?
This exponential and log stuff reminds me of half-life problems. How are half-life problems related to what we're learning?
As you know, a half-life is how long it tales for a quantity to decay by 1/2. For instance, half of the snow in your year might disappear the first day, half of the remaining amount to second day, half of the remainder the third day, etc. If this pattern were to continue (and isn't it a good thing that it doesn't?), we would consider 1 day the half life of the snow.
Now consider the exponential formula A = P (1/2)^(t/Half-life).
The initial amount P is cut in half once for every half-life of time.
Example: If the amount of bubbles in the sink is halved every 1/4 hour, then how much is left after 45 minutes?
A = 1 * (1/2)^3 The "3" comes from three half lives = 45 minutes.
A = 1/8 of the original amount
You have lots of worksheets for logarithmic and exponential word problems, equations, and inequalities to use for practice. Answers are posted outside the classroom.
