Expand Your Knowledge: Logarithmic Transformations, Exponential Growth Model Let x= day of...

Expand Your Knowledge: Logarithmic Transformations, Exponential Growth Model Let x= day of observation and y= number of locusts per square meter during a locust infestation in a region of North Africa.

x	2	3	5	8	10
y	2	3	12	125	630

(a) Draw a scatter diagram of the (x, y) data pairs. Do you think a straight line will be a good fit to these data? Do the y values almost seem to explode as time goes on?

(b) Now consider a transformation y’ = log y. We are using common logarithmsof base 10. Draw a scatter diagram of the (x, y’) data pairs and compare this diagram with the diagram of part (a). Which graph appears to better fit a straight line?

(c) Use a calculator with regression keys to find the linear regression equation for the data pairs (x, y’). What is the correlation coefficient?

(d) The exponential growth model is y = ab^x. Estimate α and β and write theexponential growth equation.