Exponential Equations

The link above will take you to the Pre-Calculus site on Logarithms. Logaritms is a tool we use to solve exponential equations. As with all of our other studies, we will begin with graphing exponential equations, then we will move to solving them for particular values.

Graphing an exponential equation will be just like graphing any other equation we have studied so far. You can start with a table of values. Eventually we will notice some patterns and be able to graph by inspection of the equation. Let's start with a few characteristics of all exponential equations.

1.They pass through the point (0,1).
2.D: {all real numbers}
3.R: (0, ∞)
4.They have y=0 as an asymptote.

Of course we can apply other translations to exponential functions just as we have with every other function we have studied. I strongly recommend completing example 2 in the module to get a feel for the other types of translations.

Once we have developed some comfort with these equations we will begin to solve for x. We have already seen this type of question (take a look at example 1) by finding a common base. Try the following one if you like.



After we are familiar with exponential equations and their graphs we will solve equations that do not have a common base.

PC40: Exact Values and other fairly precise stuff.

The link here provides a nice introduction to a few of the concepts we're working with in this module. If you follow the links on the left sidebar the site goes on to explain some other things that we will be covering very soon. Be sure to check out the PC40 Explained site for some definitions and examples as well.

Precalculus 20: Back in the saddle...exponentially.

Whew! The last unit was a bit tough at the end but it's over for now. Today we revisit an old topic: Exponents and Negatives (otherwise called Integral Exponents). If you follow the link you'll find a short explanation with plenty of examples.

By the way...I found a new website for math help. I don't know if you've tried the others yet but this one has exponent help here

Physics 11: ...and now ladies and gentlemen, the formulas.

Ah yes, the graphing thing is over, but it leads to our next step....using equations to solve problems involving motion. The link introduces four equations you will need to be able to use but there is a fifth equation that is usuful sometimes. You can find it in section 2.3 of your book.

Just remember that two of these equations are simply expressions of either the slope of a graph, or the area under the curve. The others are found by substituting expressions from one equation into another.

One more thing...who is this? (hint: despite the hair...not from the 80's)

Physics 11: Thanks for the link!

So this is a link that sort of demonstrates what we were trying to understand today about the difference between average and instantaneous velocities. There's a lot of math stuff that you need not worry about, just scroll down and take a look at the animated graph (it's the third graph with the moving green line).

As the two points move closer together you move towards a more accurate value for the instantaneous velocity.

Physics 11: Our first lab!

Over the last week we've been learning how to work with graphs of distance vs. time, and velocity vs. time. Now it's time to try it out for ourselves. You've been given two sets of data. One is distance vs. time and the other is velocity vs. time. What I'd like you to do now is:

1. produce a graph for each set of data
2. from the distance vs. time graph determine the maximum velocity (slope of a tangent line), average velocity (total distance divided by total time), and total displacement.
3. from the velocity vs. time graph determine the maximum velocity, and displacement (the area under the line).

Be sure to follow the guidelines we copied into our notes about what a good graph looks like and show your work and calculations on a separate page for each graph (If it's organized with titles it's so much easier to mark).

Also, be sure to add a paragraph or two describing the motion and what you sort of graph you should get (Theory section). Compare the data in relation to the motion you obsevered in class (not all of the data will make sense at first...explain why-Discussion section). State the values you calculate (Conclusions). Good luck.

Pre-Calc 20

The simplification of radical expressions can be difficult when you first start to work with them (as most things in math can be). The link (click on the title of this post) will take you to an explanation in PurpleMath which might be helpful. The pages that continue on are topics we will cover eventually so don't be worried if you move on through the pages and none of it makes sense...we just haven't talked about it yet.

As I mentioned to the PC 40 class, we'll be needing a quiz before long...I was thinking Friday.

Physics 11: Graphing Motion

I hope the demonstration in class today was helpful. I know some of you would like some more practice and explanation before we move on. I found this website (follow the link from the title of this post), which might help explain some of the things we've been discussing in class. The site is good, but can take a little while to load so be patient...it's worth the wait. It even has a few questions you can answer at the end to check your understanding.

Pre-Calc 12: Horizontal & Vertical Stretches and Compressions

I did a little digging around in PurpleMath and found this site. It explains things pretty well if you were needing a little extra explanation before tomorrow. If you follow the four different pages, it follows up with a little quiz at the end too. Let me know if you give it a try.

Oh, we'll be needing a quiz before long as well. I was thinking Friday.

Help for Math Students

Often when I work with a class and try to find another way to explain something, I discover something new. During the last few years I have been using Google to find study solutions for my students. Today I found PurpleMath.

I haven't had a chance to go through it in detail, but for the topics I'm currently covering, and the ones I expect to cover soon, this website does seem to have what you might be looking for. If you happen to come across another site you have found helpful let us know and share.

Physics 11

Graphs give us a great deal of information. We can read values from them, determine their slope, or find the area under the curve. For now we will work mostly with slopes of distance vs time graphs (which give velocity), and areas under a velocity vs time graph (which gives displacement).

As I mentioned today, we'll plan to have a quiz on Thursday which will include homework assigned up to now and tomorrow. Make sure you're up to date.

Pre-Calculus 20

Today we discovered how important it is to write polynomials in decending powers of x, especially when dividing. It's important to add missing terms in with a coefficient of 0. Be sure to get some extra practice in if you're unsure of how to do this...there'll be a quiz soon.

We also started looking at radicals and that if we treat them just like variables we can add and subtract them just like terms in algebra.

Tomorrow we'll look at finishing up the division of polynomials and move on to working with radicals.

Physics 30: Unit Analysis

The idea of unit analysis is simply to convert from one set of units to a more usful set of units. You may be working on a question that has some information in m/s and other information in km/h. Unit analysis lets us change one form of units to another set of units. Take a look at example #2 on page 10.

Unit analysis also lets us do more complex problems as well (like example #3).

The key to working with units is to ensure that you set up your numbers as fractions and include the units. Once you do this, the next coversion factor you need will be the one that reduces the previous unit in the numerator to 1 (see in example #2 how the red lines cross out the units you don't want).

Welcome Back

Hello everyone...I'm guessing we're all back to the business of learning this time of the year. Whether it's at work or in a classroom we're always learning...at least that's what I've found, but then for me the classroom and work are the same.

Wishing you all the best and hoping you'll stay tuned to let us know how you're doing. As always, if you run across something you feel would be of interest to math or science don't hesitate to submit it for a review.

All the best.

Answers to Chapter 20 Supplemental Problems

For Physics 30:

Chapter 20 Supplemental Problems

1. F/4
2. 4F
3. 1.0 x 10^-5 N
4. 8.0 x 10^-5 N
5. 6.25 x 10^18 electrons
6. +9.0 x 10^3 N
7. -1.1 x 10^2 N, the force is attractive
8. +44 N away
9. -9.2 x 10^-16 N
10. +2.5 N
11. 2.0 x 10^-10 C
12. -9.7 x 10^-6 C
13. 7.4 N to the left
14. 6.7 N at 7.2 degrees to the left of vertical

Come and see me tomorrow at noon if you're having any difficulties.

Calculus for the spring time....

Got to hurry folks...if you're going to finish that is. You'll need to see me after this one for a quiz I think.

More Calc....

Another Calculus Assignment

More to follow...Come and see me when you finish your review.

Calc#107

The last one for the review topic. Come and see me when you complete this one.

Calc#106

Welcome back everyone! Hope you had an enjoyable break. I'll be posting assignments more frequently now so be sure to keep up and see me with any difficulties you may be having.