Question

A famous disease control scientists is trying to determine the potential infected population of the new west Columbia flu. two weeks ago, the first patient showed up with the disease. four days later, the disease control center in Atlanta had ten confirmed cases. the scientists estimates that it will be another two days before a cure will be ready, a total of 16 days from the first confirmed case. how many patients will be infected two days from now?    what is the daily growth rate of the disease?                      how many patients will be infected two days from now?

Answer 1

It took 4 days after the first reported case for 10 people to be confirmed of the flu.

so in 4 days the contamination have spread 10 times.

It is going to be 16 days from the first confirmed case to the day they start curing people.

Assuming the contamination spreads to 10 times every 4 days, we have 16/4 = 4 time intervals for theiflu to grow ten times each.

No of patients infected in 16 days(2 days from now) = [((1*10)*10)*10)*10] = 10⁴ = 10,000..

Daily growth rate in the mean time N_t = N₀ * (1+r)^t = 10000 = 1*(1+r)¹⁶  

10000 = (1+r)¹⁶

10⁴ = (1+r)^4*4

10= (1+r)^4.

1+ r = 10^-4

^{r = 9.9999}