Chapter 4.2, Problem 23P

Expand Your Knowledge: Logarithmic Transformations, Exponential Growth Model Letx = 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 $\left(x,y\right)$ 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 $$. We are using common logarithms of 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 $y=\alpha {\beta }^x$. Estimate $\alpha \text{ and }\beta$ and write the exponential growth equation. Hint: Sec Problem 22.