Sunday, May 15, 2011

Fitting Exponential Models to Data

On Thursday we learned about fitting exponential models to dada. This lesson was based a lot on graphing and lists and spread sheets, so the Ti-Inspire was crucial. We first looked at how to solve using regression without a calculator.
For example: Using the points (0,1000) and (5, 550)
you use 1,000 as the a value (because its the y intercept) and plug the rest of the equation into
a(b)^x form.
550/1000= 1000/1000x b^5 (multiply both sides by 1/5)
and b=.887.

We then moved on to using the calculator using lists and spreadsheets
1. Add lists and spreadsheets page
-Enter your data given and label the columns
2. Press menu 4,1 (Statistics, stat calculations) then A (exponential regression)
3. Choose your x and y values
4. There should be a table of values including A, B and the function has been stored as f(1) for later use.

To graph and plot the points:
1. Same as above, add a lists and spreadsheets page and enter your data
2. Then press Control i to add a Data and Statistics page
-Here we choose our x and y value to make the scatterplot
3. Click menu 4, 6 (analyze and regression) and then 8 (exponential)
-The scatter plot will appear along with the equation

We have a quiz tomorrow on 9.1-9.4 (Monday May 16th)
What we've also covered:

-Exponential Growth/Decay: y=ab^x
Domain: All reals
Range: y:y>0
Growth:b>1 (when plugging in growth factor remember to add a 1 to the beginning of the percent and turn into decimal...ex: 6.6%=1.066
Decay: 01 (when plugging in grown factor remember to subtract the percent from 100...ex: 88%=.12)

-Continuous Growth/Decay
General function: N(t)=Ce^rt
Continuously compounded: (ONLY if it says continuous in the problem): A=Pe^rt

-Compound Interest
*if it is a growth its a positive number for r, if its decay, r is negative

-Half Lives
Example problem: The half life of Carbon-14 is 5,730 years. If an organism had 8 grams of Carbon-14 and has been dead for 28,650 years, how many grams of Carbon-14 are left?
explanation: You have to divide the 28,650 by the 5,730 to get the half life. The answer is 5 so you think about the original 8 grams that you have to cut in half 5 times. If you divide 8 by 2 five times, you end up with 1/4.

The homework is the Review assignment #1 for 9.1-9.4 and quiz monday!

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