1. 4.1 Modeling Nonlinear Data

2.  Create scatter plots of non linear data  Transform nonlinear data to use for prediction

3.  Exponential Function:  Power function:

4.  To show exponential growth: ◦ We look for a common ratio ◦ Notice the common ratio is about 3! xyratio 13 28.78.7/3=2.9 326.926.9/8.7= 3.09 482.682.6/26.9 =3.07 52402.91

5.  Linear- increases by a constant (slope)  Exponential- increases by a ratio

6.  The following table shows the heights of a Pasfor tree after 5 months. Graph age vs. height. (L1 vs. L2) Notice the graph shows an exponential growth model xy 13 28.7 326.9 482.6 5240

7. Remember, we can’t find correlation or a regression line unless the data is linear. So how do we do this? Take the logarithm of y. In L3= log (L2) Now graph (x,log y)= (L1, L3) What do you notice? The data is linear!!! So now we can use it to predict! (L1) x (L2) y(L3) log y 13 28.7 326.9 482.6 5240

8. If a variable grows exponentially, its logarithm grows linearally. ** this question will be a multiple choice on your test. For example:  The oil production per year shows an exponential increase in productivity. How would you predict data using this model?  A) Graph the year versus oil production  B) Graph the logarithm of year versus oil production  C) Graph the year versus the logarithm of oil production  D) Graph the logarithm of year versus the logarithm of oil production  E)We can’t predict data of exponential growth. Answer: C) Graph the year versus the logarithm of oil production

9. The following data is a power function.  When does a power law become linear? Take the log x and log y in L3 and L4 Then graph L3, L4 :(log x, log y) What do you notice? It’s linear!! lengthweight 12 217 353.1 4129.2 5248.7 L1L2L3 (Log L1) L4 (log L2) 12 217 353.1 4129.2 5248.7

10.  What do we need to actually know from section 4.1?  If data grows exponentially- graph (x, log y)  If data grows to a power function- graph ( log x, log y) That is it!!!! So don’t stress too much about this section-if you know these 2 facts, you are good!