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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Wednesday, September 21, 2005

### MORE logs

HALFLIFE, AMOUNT OF SUBSTANCES and POPULATION -> these are the things we discussed today that greatly involved logarhythms. In solving 'the halflife of a certain substance', 'its amount that will remain in a particular time', and 'the exponential growth of the population of a specific country' we used these formula:
 A = A0 Mt/p

used in a problem with lots of information

where A is the final amount, A subscript 0 is the original amount, M is the multiplication factor, t equals time and p is the period

 A = A0 (MODEL)t

used in a problem with little information
where (MODEL) is the model for the growth of a certain substance

Now that we already have the formula, we can now build an equation using the given figures of the problem. But then again, life can be so tough as not knowing what to do when you have to solve an equation that looks like this:

 0.1 = 153 (1/2)t/112500

Then here comes Mr. K to the rescue as he gives us the basic rules in solving logarhythms:

For MULTIPLYING logarhythms with the same base we use:
(simply adding the result of M and N)

 Log b MN = log b M + log b N

For DIVIDING logarhythms with the same base we use:
(just as if subtracting the result of N from M)

 Log b M/N = log b M - log b N

For logarhythms raised with EXPONENTS we use:
(multiplying the exponent to the result of M)

 Log b MC = C log b M

and the CHANGE OF BASE rule:(this im having a hard time to explain (^.^) )
 Log b M = log a M log a B

so... ok , that's it. I think that's about it. Those were all the stuff i learned today in Calculus. LOGARHYTHM RULES.

and now it's time to pass the torch to.... STEVEEEEEEEE. =)