TPC: Logarithmic Graphs: Log Regressions. Due Feb 27

In your last blog, you were asked to try to graph a set of numbers on a standard unit piece of graph paper. The values became large quickly and it was impossible to put all the values on the graph at the same time.  Some of you discovered the log graphing tool; some of you remember the blog from last year.  Here's a new twist. We will use data on distance from the sun to help us see the usefulness of logs. 

This is an example from your text: Larson, Precalculus (2007).  

The data below is each planet's distance from the sun in Astronomical Units ( 1 AU is the distance from the sun to our Earth) and the length of time it takes to orbit the sun in terms of our year.

Find a LINEAR equation that expresses the relationship between x and y. Notice that the table seems to suggest that you need to put "x" in L1 and "y" in L3.  Please do that.  Start by scatterplotting the following data. What’s the scatterplot look like? Then Stat-calc-linreg L1 vs L3. You'll see the line fits the data pretty well, but that the data appears to be more on a concave up curve, like an exponential function. None of the points fall exactly on the line. 

Take the natural log of each x and each y; put "lnx" in L2 and "lny" in L4. (You can do this quickly by placed the cursor at the top of L2, and typing "lnL1" as a formula then the down arrow; then put the cursor at the top of L4, then type "lnL3" then a down arrow. )  Then scatterplot lnx versus lny (in other words, scatterplot L2 vs. L4). What do you observe?  Now either run a linear regression of the lnx and lny data or choose any two points to find the slope. 

Explain what you discovered in your blog; take photos or snips of your calculator image to help you explain.