During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by the following.
Q(t) =
7000
1+249 eā0.6 t
(a) How many children were stricken by the flu after the first day?
(b) How many children had the flu after 10 days?
(c) How many children eventually contracted the disease?
To answer these questions, we need to use the given equation:
Q(t) = 7000 / (1 + 249e^(-0.6t))
(a) To find the number of children stricken by the flu after the first day (t=1), we can substitute t=1 in the equation:
Q(1) = 7000 / (1 + 249e^(-0.6*1))
Simplifying the expression:
Q(1) = 7000 / (1 + 249e^(-0.6))
You can calculate this using a calculator or any mathematical software. The result will give you the number of children stricken by the flu after the first day.
(b) To find the number of children with the flu after 10 days (t=10), we substitute t=10 in the equation:
Q(10) = 7000 / (1 + 249e^(-0.6*10))
Simplifying the expression:
Q(10) = 7000 / (1 + 249e^(-6))
Again, use a calculator or mathematical software to calculate the expression and get the number of children with the flu after 10 days.
(c) To find the number of children who eventually contracted the disease, we need to observe what happens as time approaches infinity. Notice that as t grows very large, the exponential term (e^(-0.6t)) approaches zero. Therefore, as t approaches infinity, Q(t) approaches:
Q(ā) = 7000 / (1 + 249e^(0))
Since e^0 is equal to 1, the expression simplifies to:
Q(ā) = 7000 / (1 + 249)
Calculate the expression above using a calculator or mathematical software to find the number of children eventually contracting the disease.