Cooper Section 8.5 #5
The number of people who will develop an infectious disease depends on the percentage of people inoculated. If $x$ is the percentage of people inoculated, then $f(x)$ people get the disease.
a. What does $f(0) = 10^6$ mean?
A. For each additional 1 percent of the population that is not inoculated, 1 million more people get the disease.
B. When 1 million percent of people are inoculated, then no one gets the disease.
C. When no one is inoculated, for each percentage of the population that gets an inoculation, the number of people who get an infection goes down by 1 million.
D. 1 million people will get infected regardless of what percent of the population is inoculated.
E. When no people are inoculated, then 1 million people will get the disease.
b. What is the meaning of the statement that $f'(50) = -10^4$?
A. 10,000 fewer infections occur for every increase of 50 percent in the inoculated population.
B. At 51 percent inoculation, 10,000 fewer infections occur.
C. 10,000 fewer infections occur for every increase of 1 percent in the inoculated population.
D. At 49 percent inoculation, 10,000 more infections occur.
E. 50 fewer infections occur for every increase of 1 percent in the inoculated population.
F. When 50 percent of the people are inoculated, the rate at which infections would decrease is 10,000 infections per inoculated percentage of the population.
c. What does $f^{-1}(100) = 85$ mean?
A. 100 people get the disease when 85 percent of the population is inoculated.
B. When 100 percent of the people are inoculated, the number of infections increases by 85 for every decrease of 1 in the percentage of people inoculated.
C. 85 people get the disease when 100 percent of the population is inoculated.
D. When 85 percent of the people are inoculated, the number of infections decreases by 100 for every increase of 1 in the percentage of people inoculated.