Question

A few weeks into the deadly SARS (Severe Acute Respiratory Syndrome) epidemic in 2003, the number of cases was increasing by about 4% each day.† On April 1, 2003, there were 1,804 cases. Find an exponential model that predicts the number of cases t days after April 1, 2003. f(t) = Use it to estimate the number of cases on April 26, 2003. (The actual reported number of cases was 4,836.)

Answer 1

`f(t)=1804(1.04)^(t)\\f(25)=4809.17`

Explanation:

1. Since the increasing rate is 0.04 or (4%) per day, then the factor is (1+0.04) raised to t days, and we have and exponential growth therefore we can write:

`\\f(t)=c(1.04)^t\\f(t)=1,804(1.04)^t\\`

2. To estimate the number of cases, 25 days later following that exponential model

`f(25)=1804(1.04)^(25)\\f(25)=4809.17`