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 A(t) of people infected t days after April 1, 2003.

Answer 1

Answer:

Therefore the required exponential model is

$A(t)=1,804(1.04)^t$

Explanation:

The exponential function

$A(t)=Ab^t$

Given that, the number of cases of epidemic increases by 4% each. The number of cases was 1,804 on April 1, 2003.

Now we consider the exponential function

$A(t)=Ab^t$

The initial condition is when t=0, A(0)= 1,804

1,804 = Ab⁰

⇒A=1,804

The number cases increases at a rate 4% each day.

∴ b= (1+4%)

      =1+0.04

     =1.04

Therefore the required exponential model is

$A(t)=1,804(1.04)^t$