## Monday, April 7, 2008

### Intro to Exponential Functions

Hi everybody this is benofschool and here is today's scribe.

Well we're back from spring break and everybody is ready to do some math! Just as a reminder everybody's Flickr pictures are due on the midnight of Friday. Just post a direct link to your Flickr page onto the blog. Remember to tag it with your name, flickr, and trigonometry. For the picture do not contrive it or draw it and say that it is math. It is math but it isn't naturally occuring. The picture must exist as it is naturally. One example of a contrived shot would be a drawing of a parabola on a piece of paper. It is drawn but a natural one would be on that I had taken last year:
My picture wasn't contrived as in I didn't draw a parabola on the floor but I saw a parabola on this chair. I hope that explained everything. Okay back to our new unit.

Well we continued on what we did on the last day of class before spring break. We were asked to find other ways to write down several numbers with exponents and only exponents. Mr.K showed us many examples such as using negative exponents. Like in grade 9 math, negative exponents means find the power of the reciprocal of the number. For example:

The number 4 could be written as 16 to the power of 1/2 which is the same as the square root of 16. The second example 1/16 is a fraction so to get from that into a number with a denominator of 1 instead just use a negative exponent to get the reciprocal of 1/16. Then rest of the exponent says 1/2 meaning to get the square root of 16 which is 4. As a reminder of exponents and powers lets look at this picture of the anatomy of a power:

So a is the base which was 16 in the example above, b is the exponent which was 1/2 above and c is the power which is the result, 4.

Okay after find some of those we went back to solving for x but x was in a different place. x was an exponent. If you look at the slides 4 and 5 x is in the exponent spot. So to solve these just try to get the same base on both sides by using the techniques used to find other forms of numbers in exponents like earlier explained. When that is complete since the bases are equal then so must the exponents. So seperately just solve for x like in basic algebra if needed. Sometimes you end up with an algebraic expression like 2x-1 as an exponent. So if the base that has that exponent needs to be changed into another base make sure to multiply the new exponent into 2x-1. Then again solve for x.