1. The RMU community of 3,000 people is homogeneously mixed. Assume that one person (staff or student) returned to the community with COVID-19. There exists a mathematical model, which assumes that diseases tend to spread at a rate in direct proportion to the number P who have the disease and to the number 3, 000 − P who have not yet contracted the disease (logistic growth). The mathematical model i, P(t) = 3000 1 + 2999e −1.2t where P(t) is the number of people who have contracted the disease after t days. (a) How many people would have contracted the disease after 5, 10, 15, 20, 25 and 30 days? (b) How many days will it take until half of the community to have contracted COVID-19? (c) How many days will it take until the entire community contracts COVID-19?
1. The RMU community of 3,000 people is homogeneously mixed. Assume that one
person (staff or student) returned to the community with COVID-19. There exists a
mathematical model, which assumes that diseases tend to spread at a rate in direct
proportion to the number P who have the disease and to the number 3, 000 − P who have
not yet contracted the disease (logistic growth). The mathematical model i,
P(t) = 3000
1 + 2999e
−1.2t
where P(t) is the number of people who have contracted the disease after t days.
(a) How many people would have contracted the disease after 5, 10, 15, 20, 25 and 30 days?
(b) How many days will it take until half of the community to have contracted COVID-19?
(c) How many days will it take until the entire community contracts COVID-19?
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