• Discussion of some homework problems (Exercise 15.1 parts 1, b, c)
Here is something that came up in (c):
* We need to know how to interpret what the calculator is telling us. In particular, when the result of a calculation is given in scientific notation, you should not just write down what you see on the screen, but interpret it as a number (in decimal form preferably, if possible, but otherwise in proper scientific notation).
• Applications of exponential functions: word problems
Please note, the methods and formulas we use follow one of several methods that you may find if you search the web (or talk to other people). Be careful to use our method and not some other method, because you may get wrong answers using the other methods. (The methods differ based on what type of information is given in the problem and what base is used for the exponential function.)
In particular: do not use any method which uses a “continuous rate of growth”, and do not use any method where the base of the exponential function is required to be e. To be safe, use your textbook or the links that I will provide as your resources.
We worked through Examples 15.2 and 15.3 in the textbook. Make sure that you understand how we got our exponential functions from the given information in the word problems, and how we solved the other parts once we had the exponential functions.
The next thing we will be working on (aiming at the kind of problems that will be on the Final Exam) is finding exponential function if we are given a rate of growth or decay per unit time, and using those to find out when a quantity will double or triple or become half tis original size, etc.
To make this easier, you can prepare by viewing the videos linked in the homework section. I have specifically chosen those videos because they use our method. Please do not go searching for other videos, they almost certainly will be using the wrong method for our problems!
• Review the examples discussed in class. We did not finish Exercise 15.1(c), which was assigned last time, and you should certainly complete it!
• Do the (short) WeBWorK “Exponential Function Applications”. You do not need to do the other one at this time.
• Also, from the textbook, do Exercises 15.2 and 15.3. You may put one on the board next time, after the quiz, if you like.
• To prepare for next time, view the following videos which show how to find an exponential function if you are given a rate of growth or decay:
An exponential growth problem by PatrickJMT – it’s just one example, but he shows the relationship between the form of the exponential function we have used so far and the form where you are given a rate.
Exponential growth word problems by Kevin Dorey (It’s YouTube, so be warned that the next video may autoplay right after this one. You’ll want to turn off autoplay.)
• There will be a quiz next time: the topic will be exponential functions, problems like Exercise 15.1(a-d)
• Don’t forget to fill out the Post-Test survey which I handed out in class. (not to hand in: this is just for yourself) Doing this kind of reflection has been shown to improve test grades!
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!