Thursday, March 15, 2007

9.4 Exponential Growth and Decay

Relative Rate of Growth: Things are growing based on what you already have.
  • Constant change based on what you start with


1. Separate the variables


2. Take the integral of both sides


3. Evaluate the integral (take the antiderivative).
Don't forget to add +C!


4. Come up with an equation for P (Isolate P).


This is a constant and the initial value:


P = population
P sub o = initial
K = constant
t= time


To find value of K:


Half-Life: Rate of decline or breakdown.

The (.5) is the rate at which the substance declines or breaks down.

I am going to use the carbon-14 (C-14) example even though we did it in class because it makes sense to most people after taking Bio and Chem.


Example Problem: EXPONENTIAL GROWTH


Newton's Law of Cooling:
Difference between an object and its surroundings.
Ok now that I totally get this (and so does Genny!) here goes:


Data:
mac and cheese (that is what I am eating right now) at 110 F.
Room at 68 F.
30 minutes later, the mac and cheese is at 100 F.
Find the temperature after 1 hour.
1. Set up specific equation

The ratio inside of ln is (later data point)/(original data point).
The units for time do not matter as long as you are consistent.

2. Solve
Plug in 60 for t.

3. Add T sub o to the answer in part 2. (This is the typical mistake that people make, at least Genny and I did)
Add 68 to the answer in part 2.

Sorry I could not put this up sooner. I realize you may have needed it last night, but I did get it done and I really was not sure if I could. Thank goodness blogger was nice to me today.

Here is a good website. It is the one that Dartmouth uses for its books I think:
www.math.dartmouth.edu/~klbooksite/3.02/302.html

AND MR FRENCH NO ONE IS NEXT...CAN YOU BELIEVE IT?

I have been a die-hard OC fan since the beginning, even when it went kinda crazy. It is strange that today is a Thursday and there is no OC two weeks in a row. In memory of what was once one of the best shows to ever hit television:



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