Applications of the litter formula: This is a continuation of Exercise 10. Here we make use of the formula A = R − Re−kt obtained in the previous exercise. a. Show that 95% of the limiting value is...

Applications of the litter formula: This is a continuation of Exercise 10. Here we make use of the formula A = R − Re−kt obtained in the previous exercise.

a. Show that 95% of the limiting value is reached when t = 3/k.

b. A study46 of sand dune soils near Lake Michigan found the decay rate to be k = 0.003 per year. How long is required to reach 95% of the limiting value?

c. The decay rate for forest litter in the Sierra Nevada mountains in California is about 0.063 per year, whereas the decay rate in the Congo47 is about 4 per year. How does the time required to reach 95% of the limiting value compare for the Congo and the Sierra Nevada mountains?