Question

A new virus strain starts out with one infected individual and passes on to others in such a
way that the number of infected individuals triples every four days. Assume that there is no
deterrent for the spread of the virus.
(a) Set up an appropriate modelling function to determine the number of infected individuals
t days after the outbreak.
(b) Determine how many individuals will be infected 10 days after the outbreak.
(c) Determine how long it will take for the number of infected individuals to reach 100,000.

Answer 1

(a) Every 4 days, the infected people are multiplied by a factor of 3. Hence, to find the infected people on the Day t starting from day zero, we should divide the number of days by 4 becaue that is how many peiods were there, when the infected population gets multiplied by 3. And then, we should raise 3 to this power to obtain total infected people. Hence, The appropriate model is of the type

where it is given that x(0) = 1, hence the model actually simplifies to

(b) We shall get a decimal value by putting t = 10 in this formula. Hence, e shall take the rounded integer value.

(c) We need to substitute x(t) = 100,000 and use logarithms to find the nearest integer value of t

Hence, in 42 days the ifected people shall cross 100,000 and in fact, the predicted value is