is not fully simplified, and should be further simplified to:
Mr. O'Brien also emphasized that we should use "=" only when the equation is completely equal, and "≈" if the equation is approximately equal. For example, if you have the equation x = 12/13, the equals sign is appropriate. But if you make 12/13 a decimal, it should be written as x ≈ .923 because the decimal is being rounded. He also pointed out that people were losing points for not following directions (for example, rounding to four decimal places when the problem specified to round to three decimal places).
He also explained problem #9 in detail, as follows:
ln 4x = 14/13 can be rewritten as
either by thinking of it as just directly translating it into this form, or by making each side of the equation raised to a power of e, like this:
He then explained checking it without a calculator. He also said to beware of extraneous solutions for our test. A problem can be done perfectly correctly, but then the solutions can be extraneous. This means we should be careful to check our answers by substituting the values back into the equations. He later said how we need to use common sense in checking our answers. For example, if we're doing a carbon dating problem and we get a negative answer for the time, there's obviously a problem with our math.
We then went to p. 270 of the textbook, which went over all of the things we're expected to know for the test. The themes of the test are the basics, as well as real-life problems. Note: we do not have to "recognize the five most common types of models involving exponential and logarithmic functions". We have to be able to use things from section 3.5, but we don't have to have them memorized.
After this, we reviewed homework questions. Mr. O'Brien talked about how, in order to minimize the amount of time we spent on problems during math tests, we should go through the problems to see if there are things we can recognize. For example, repeated calculations can use the "function machine" on our calculators. (Enter the function into the y= on our calculator, and then use a table that's set to ask for the independent variables.)
He also reviewed the correlation between
with the first equation being used for daily, monthly, yearly, etc. compounding, and the Pert equation being used for continuous compounding. (We will not need to have these equations memorized for the test).
Then we reviewed using the [STO→] key to store long values to letters in our calculators. To store a value (for example .56273) to a letter (or example A), type [.56273][STO→][ALPHA][A]. Then to recall the value, simply type [ALPHA][A].
Remember that % decrease is (amount of decrease/total amount). The amount of decrease is the difference of the two values.
For homework, we have to correct all our homework to turn in next class, do 8 problems from the Chapter 3 Review Test to include with our homework packet, and revise for the test next class. Mr. O'Brien said that the test will have a lot of word problems.
Scribe for next class is Andy.
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