Wednesday 15 November class (Updated)

Posted on November 19, 2017 by Sybil Shaver

(After Test 3)

 

Techniques we will need for applications of exponential functions:

Solving for an unknown exponent

Example: find x if 4^{x} = 57

Solution: take the logarithm of each side. Any base will do. We will use the natural logarithm.

\ln\left(4^{x}\right) = \ln(57)

x\ln\left(4\right) = \ln(57) by the “log of a power” property

x = \frac{\ln(57)}{\ln\left(4\right)} divide both sides by \ln(4)

This is the exact value. We will approximate it using a calculator. x\approx 2.916

 

 

Solving for an unknown base (integer exponent)

Example: Find b if b^{15} = 60

Solution: we solve by taking the 15th root, which is the \frac{1}{15} power:

b^{15} = 60 b = 60^{\frac{1}{15}} \approx 1,314

 

We discussed Example 15.1 parts a, b, and c. These show how we will go about translating word problems into math language in the applications of exponential functions we are about to do.

Homework:

• Review the methods we used in these examples. We will need to use these (and other things we already know who to do) in working the application problems.

• There is no very good WeBWorK on this. You should do Exercise 15.1(a-d): I will ask for volunteers to put these on the board next time.

• Make sure that you finish the WeBWorK that was previously assigned!

• No Quiz next time, but do make sure you are prepared and know how to work exercises like Exercise 15.1, so we can go ahead and work the application problems!

• The Test 3 solutions are in this separate post, along with a Post-test Thinking Strategically survey. It will be very worth your while to fill out the Post-test survey even if you did not fill out the pre-test survey!

 

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!

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