Suppose that a communicable disease has an infection stage and an incubation stage (like HIV and AIDS). Assume that the infection rate is a constant people per month and the incubation distribution is
month-1. The rate at which people develop the disease at time
is given by
people per month. Use your CAS to find expressions for both the rate
and the number of people
who develop the disease between times
and
. Explain why the graph
has a horizontal asymptote. For small
's, the graph of
is concave up; explain what happens for large
's.
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