Let g(t) = 100 - 100 $e ^ { - 0.01 t }$ be the number of cases of measles in a certain school t days after the first case is reported. Which of the following best describes the spread of the disease?
A) The number of cases decreases according to exponential decay.
B) After the first day there are 100 cases, after which the number of cases decreases daily to 0.
C) Initially, the disease spreads quickly, but then the rate of increase slows so that the number of cases never exceeds 100.
D) The disease spreads quickly until the number of cases reaches 100; then gradually the number of cases decreases.
E) none of these

Question

Quizplus · Accepted Answer

The function g(t) = 100 - 100e^(-0.01t) represents exponential growth towards a limiting value of 100 cases. Initially, the number of cases increases rapidly as t increases, but as t becomes very large, the term 100e^(-0.01t) approaches 0, making g(t) approach 100. This means the rate of increase slows down as the number of cases approaches 100, but it never actually exceeds 100.

Let G(t) = 100 - 100 e−0.01te ^ { - 0.01 t }e−0.01t

Let G(t) = 100 - 100 $e ^ { - 0.01 t }$