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.
A(t) = 1804(1.04^t)
Use your model to estimate how fast the epidemic was spreading on April 17, 2003. (Round your answer to the nearest whole number of new cases per day)

Answer 1

The exponential model to predict the number of people infected t days after April 1, 2003 is A(t) = 1804(1.04^t). Estimating how fast the epidemic was spreading on April 17, 2003, the approximate number of new cases per day is 105.

Step-by-step explanation:

To find an exponential model that predicts the number of people infected t days after April 1, 2003, we can use the formula:

A(t) = 1804(1.04^t)

Where A(t) represents the number of people infected and t represents the number of days after April 1, 2003.

To estimate how fast the epidemic was spreading on April 17, 2003, we can calculate the difference between the number of cases on April 17 and April 16. Let's do the calculation:

A(16) = 1804(1.04^16) ≈ 2507.25

A(17) = 1804(1.04^17) ≈ 2612.80

The estimated number of new cases per day on April 17, 2003 is the difference between A(17) and A(16), rounded to the nearest whole number. Let's calculate:

New cases per day = A(17) - A(16) ≈ 2612.80 - 2507.25 ≈ 105

Therefore, the estimated number of new cases per day on April 17, 2003 is approximately 105.

Answer 2

How fast means rate of growing.

The rate of change (growing) is given by the first derivative of the fucntion.

A(t) = 1804 * (1.04)^t

A '(t) = 1804 * (1.04)^t * ln(1.04) = 70.75 * (1.04)^t

t = 17 - 1 = 16 days

=> A '(t) = 70.75 (1.04)^16 = 132.5 = 133 cases per day.

Answer: 133 cases per day.