The Public Health Service monitors the spread of an epidemic of a particularly long lasting strain of the flu in a city of 500,000 people using the logistic function. at the biginning of the first week of monitoring (time zero), 200 cases had been reported. During the first week 300 new cases were reported. Determine the logistic Function
To determine the logistic function, we need to analyze the data given and find a pattern or trend in the spread of the flu.
The logistic function is commonly used to model the growth or spread of populations over time. It has the following form:
P(t) = K / (1 + A * e^(-B * t))
Where:
P(t) represents the number of cases at time t
K represents the maximum capacity or maximum number of cases
A represents the initial growth rate
B represents the decrease in growth rate over time
e is the mathematical constant (approximately 2.71828)
t is the time
In this case, we are given the following data:
At time zero (beginning of the first week), there were 200 reported cases.
During the first week, 300 new cases were reported.
Using this information, we can find the initial growth rate A and the decrease in growth rate B.
The initial growth rate A can be calculated by dividing the change in cases by the initial number of cases:
A = (Change in cases) / (Initial number of cases)
= 300 / 200
= 1.5
Now, let's find the decrease in growth rate B. The decrease in growth rate can be estimated by observing the data and how it changes over time. For this, we need more information about the number of cases reported in the subsequent weeks. If you have that information, please provide it and we can continue the calculation.