(1 point) A infection originated from an unknown pollution can kill 80 percent o
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Question
(1 point) A infection originated from an unknown pollution can kill 80 percent of those who are already ill and make 40 percent of the healthy population ill each month. Assume that everyone is healthy initially and the death rate of the healthy population is negligible. a. Suppose that no one who is infected can become healthy again. Find the percentage of the original population that will die in the next four months. percent b. It is found that a type of treatment can cure 10 percent of the infected population and reduce the death rate of the infected population to 60 percent each month. Find the percentage of the original population that will die in the next four months. percent the percentage of the original population that will die in the next four months. Note that in this question, you will need to introduce an additional subgroup for the population that is immune. percentExplanation / Answer
a) Initially all of them were healthy.
After 1st month : 60% became ill. 40% still healthy.
After second month : 60×80%=48. 48% of the total population will die after the second month.
60-48=12
40×60%=24.
24+12=36% of the total population will be ill after the second month.
Remaining healthy people =16%
Third month : 36×80%=28.8
(48+28.8)=76.8% of the total population will be dead after third month.
36-28.8=7.2
16×60%=9.6
(7.2+9.6)=16.8% of the total population will be ill after third month.
Remaining healthy people = 6.4%
After fouth month : 16.8×80%=13.44
(13.44 +76.8)=90.24.
90.24% of the total population will be dead after the fouth month.
b) Initially all of them were healthy.
After the first month : 60% became ill. 40% still remain healthy.
After the second month : 60×60%=36. 36% of the total population will be dead after the second month.
60×10%=6. 6% of the total population will be cured because of the treatment.
60-(36+6)=18
40×60%=24
18+24=42% of the total population will be ill after the second month.
Remaining healthy population(including people who were cured) = 22%
After the third month : 42×60%=25.2. (36+25.2)=61.2% of the total population will be dead after the third month.
42×10%=4.2. 4.2% of the total population will be cured because of the treatment.
42-(25.2+4.2)=12.6
22×60%=13.2
12.6+13.2=25.8% of the total population will be ill after third month.
Remaining healthy population : 13%
After the fourth month : 25.8×60%=15.48.
(61.2+15.48)=76.68% of the total population will be dead after the fourth month.
c) Initially all of them were healthy.
After the first month : 60% became ill. 40% still remain healthy.
After the second month : 60*60%=36. 36% of the total population will be dead after the second month.
60×10%=6. 6% of the total population will now be immune to the disease.
60-(36+6)=18
40×60%=24
18+24=42% of the total population will be ill after the second month.
Remaining healthy population = 16%
After the third month : 42×60%=25.2.
(36+25.2)=61.2% of the total population will be dead after the third month.
42×10%=4.2. (6+4.2)=10.2% of the total population will now be immune to the disease.
42-(25.2+4.2)=12.6
16×60=9.6
12.6+9.6=22.2% of the total population will be ill after the third month.
Remaining healthy population = 6.4%
After the fourth month : 22.2×60%=13.32.
(61.2+13.32)=74.52% of the total population will be dead after the fourth month.
Answers are a)90.24% b)76.68% c)74.52%
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