Question

An epidemic follows the curve P=200/1+20,000e^-0.549^t million people, where t is in years. How fast is the epidemic growing after 10 years? (Round your answer to two significant digits.)

Answer 1

The equation is
P = 200 / (1 + 20000 e^-0.549t)
TO get the rate of epidemic growth, we differentiate the equation with respect to t
dP/dt = -200(1 + 2000 e^-0.549t)^-2 (20000)(-0.549)
Substitute t = 10 and you will get the epidemic growth rate after 10 years