12.60 Leaf litter decay Ecologists believe that organic material decays over time according to an exponential decay model.

This is the case 0 6 b 6 1 in the exponential regression model, for which my decreases over time. The rate of decay is determined by a number of factors, including composition of material, temperature, and humidity. In an experiment carried out by researchers at the University of Georgia Ecology Institute, leaf litter was allowed to sit for a 20-week period in a bag in a moderately forested area.

Initially, the total weight of the organic mass in the bag was 75.0 kg. Each week, the remaining amount (y) was measured. The table shows the weight y by x = number of weeks of time that have passed.

a. Construct a scatterplot. Why is a straight-line model inappropriate?

b. Show that the ordinary regression model gives the fit yn = 54.98 - 3.59x. Find the predicted weight after x = 20 weeks. Does this prediction make sense?
Explain.

c. Plot the log of y against x. Does a straight-line model now seem appropriate?

d. The exponential regression model has prediction equation yn = 80.610.8132x. Find the predicted weight (i)
initially and (ii) after 20 weeks.

e. Interpret the coefficient 0.813 in the prediction equation.

Transcribed Image Text:

x y x y X y x y x y x y 0 75.0 1 60.9 2 51.8 3 45.2 4 34.7 5 34.6 6 26.2 7 20.4 8 14.0 9 12.3 11 8.2 15 15 3.1 20 20 1.4