On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 5 days for several months. As of July 27, 2009, the number of new cases was 26116. Which one of the following exponential functions model the growth of this virus?

Question

Quizplus · Accepted Answer

The exponential function for the growth of the H1N1 virus should have the form y = ae^(bx), where y is the number of cases, x is the time in days, and a and b are constants to be determined.

To find the values of a and b, we can use the given information that the number of new cases doubles every 5 days. This means that if we take the ratio of the number of cases at two different times 5 days apart, we should get a value of 2.

Let's use July 27th (day 0) and August 1st (day 5) as our first two data points. The number of new cases on July 27th was 26116. On August 1st, the number of new cases would be double that amount, or 52232.

Using the exponential function y = ae^(bx), and plugging in the values for y, x, and b (which is 1/5 since the virus doubles every 5 days), we get:

52232 = ae^(1/5 * 5)
52232 = ae

Simplifying this equation, we get:

a = 52232 / e

Now we have the value of a and can write the exponential function as:

y = (52232 / e) * e^(bx)

To find the value of b, we can use another set of data points. Let's use the number of new cases on July 27th and August 6th (day 10). The number of new cases on August 6th should be double the number on August 1st, or 104464.

Using the exponential function and plugging in the values, we get:

104464 = (52232 / e) * e^(1/5 * 10)

Simplifying this equation, we get:

e^(2/5) = 2

Taking the natural logarithm of both sides, we get:

ln(e^(2/5)) = ln(2)
2/5 = ln(2)
b = ln(2) / 5

Now we have the complete exponential function:

y = (52232 / e) * e^((ln(2) / 5)x)

Simplifying this equation, we get:

y = 52232 * 1.316^x

This equation corresponds to answer choice B.

On August 21, 2009, the World Health Organization Announced Its