Chapter 5.4, Problem 63E

Polio Immunization Polio, a once-feared killer, declined markedly in the United States in the 1950s after Jonas Salk developed the inactivated polio vaccine and mass immunization of children took place.

The number of polio cases in the United States from the beginning of 1959 to the beginning of 1963 is approximated by the function

$N(t)=5.3e^{0.095t^2-0.85t}\text{ (0}\le t\le 4\text{)}$

where N(t) gives the number of polio cases (in thousands) and t is measured in years, with t = 0 corresponding to the beginning of 1959.

1. a. Show that the function N is decreasing over the time interval under consideration.
2. b. How fast was the number of polio cases decreasing at the beginning of 1959? At the beginning of 1962? (Comment: Since the introduction of the oral vaccine developed by Dr. Albeit B. Sabin in 1963, polio in the United States has, for all practical purposes, been eliminated.)