I have this done half way but not sure of how the remaining should be handled, pleaes help me out.
The equationP = P0 (1-e-0.05T) has been developed to simulate the spread of a virus and relates the number of persons infected (P) in a population P0 , after a period of T days after it has first been detected.
Use this model to determine:
(i) The number of persons in a town with a population of 10,000 that would be expected to be infected five days after the first detection of the virus
(ii) The time in terms of number of days before 50% of the population is infected
(iii) The time in days before 95% of the population is infected.
Here is my steps:
P = 10,000 (1 – e-0.0(5)(5))
P = 10,000 (1 – e-0.025)
P = 10,000 (1- 1/e0.025)
I was stocked at how to convert 1/e0.025.
Please bail me out.
Ola
Hi,
Very grateful for your help, pls can you help me to have a look at the solutions I finally arrived at just to be sure I am on the right track:
(i)
P=Po(1-e^-0.05(5))
P = 10,000(1-^-0.25)
P = 10000 (1-0.7788)
P = 10,000(0.2212)
P = 2,212
(ii)
1/2 of 10,000 (1-e^0.05(T))
= 1/2(10,000) (1 - 0.95123T)
= 5,000 (1 - 0.95123T
= 5,000 - 4756.15T
4756.15T = 5,000
T = 5,000/4756.15
T = 1.05127
T = 1 day (aproximately)
(iii)
95% of 10,000 (1 - e^0.05(T))
= 9,500 (1 - 0.95123T)
= 9,500 - 9,036.68T
9036.68T = 9,500
T = 9,500/9036.68
T = 1.051271 day
T = 1 day (aproximately)
I accept with information:I have this done half way but not sure of how the remaining should be handled, pleaes help me out.
The equationP = P0 (1-e-0.05T) has been developed to simulate the spread of a virus and relates the number of persons infected (P) in a population P0 , after a period of T days after it has first been detected.
Use this model to determine:
(i) The number of persons in a town with a population of 10,000 that would be expected to be infected five days after the first detection of the virus
(ii) The time in terms of number of days before 50% of the population is infected
(iii) The time in days before 95% of the population is infected.
Here is my steps:
P = 10,000 (1 – e-0.0(5)(5))
P = 10,000 (1 – e-0.025)
P = 10,000 (1- 1/e0.025)
I was stocked at how to convert 1/e0.025.
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