Wednesday, April 15, 2009

April 14/09

Hello everyone. In today's class we started off talking about multiplying big numbers such as the one on the slide. Multiplying 1024*4096 in your head is difficult, so what John Napier created was instead of multiplying 1024*4096 in your head change them into a power with the same base (2^10 * 2^12) and just add the exponents together to find the answer (2^22). Here adding is a lot more easier then just multiplying big numbers.

Later we started putting together tables of value (slide #2) and found that there were patterns to how exponents work. Any base with an exponent of 0 is equal to 1, and powers with negative exponents decrease but never reach 0.

On slides 3 and 4 notice that none of the graphs doesn't go below the horizontal line unless the base is negative. If the exponent is negative it only decrease but does not become 0.
On the next slide (slide #5) something really cool happens. Notice that the base is negative and in close brackets. The slide shows what the power of (-2)^x looks like when graphed, as you move the the right it will show you the values of x but values of y will vanish.

Moving on we went into the subject of sketching the inverse of f(x)=2^(x-2) (as seen on slide# 6). First sketch the f(x)=2^(x-2) on the graph. The x,y values of what you get from the graph are switched around when you sketch the inverse. Any values that are on the blue dotted line stays the same. Slides 7 and 8 is another example.

When you put rewrite the table of values to their inverse (slide #9) their values are switched with the other.

The final discussion in class talks about the anatomy of a power and also logarithms. (slide #10) In a power there is a base and an exponent, together they are called a power. (slide# 11) In logarithms it is like the inverse of a power, there is a base and a power equalling an exponent. As it is mentioned in the slide logarithms is a power.

I apologize that I posted late and that the next scribe volunteered in class.
So thanks and again sorry i posted late


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