Final answer:
To predict an outbreak at the poultry farm, we use an exponential function N(t) = a · 2^t, where a is the initial number infected and t is time in days. Assuming only one initial case and no change in spread rate, after two days, it is unlikely that the farm will declare an outbreak as the number of infected birds would be below the 5% threshold.
Step-by-step explanation:
Exponential Function Representing the Spread of Illness
To represent the spread of illness at the farm with an exponential function, we need information such as the initial number of infected birds and the rate of infection over a given time period. Assuming the illness starts with one infected bird and the number of infections doubles each day, an example of an exponential function could be N(t) = a · 2^t, where a is the initial number of infected birds (a=1) and t is the time in days.
Let's calculate if 5% of the farm's birds will be infected after 2 days: N(2) = 1 · 2^2 = 4. Since the farm has 26,874 birds, 5% of the population is 26,874 · 0.05 = 1,343.7 birds. Clearly, 4 infected birds is well below the outbreak threshold of 1,343.7 birds.
If the rate of spread is greater than a doubling each day or if the initial number of infected birds is larger than one, this number could be higher. However, based on the given function and in the absence of additional information about the rate of infection, it can be predicted that the farm will not declare an outbreak after 2 more days assuming the spread rate remains constant and begins with only one initially infected bird.
Understanding Disease Spread
Sporadic diseases occur occasionally and at irregular intervals. Endemic diseases are consistently present in a population at stable rates. An epidemic occurs when disease cases exceed normal expectancy and start to spread rapidly within a population. If this rapid spread crosses international borders, it can become a pandemic, which is a worldwide epidemic.