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The number of people in a community who became infected during an epidemic t weeks after its outbreak is given by the function f(t)=20,000/1+ae^-kt where 20,000 people of the community are susceptible to the disease. Assume that 5000 peoeple were infected initially and 8923 

had been infected by the end of the fourth week. Complete parts a. and b

 

Find the number of people infected after 8 weeks _____?

 

 

After how many weeks will 12,192 people be infected ____ weeks??

 Mar 25, 2020
 #1
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Need to find  'k'  and  'a'

at t= 0  infected = 5000

 

5000 = 20000/(1+ae-k(0))     yields a = 3

 

Now find 'k'

At t= 4    infected = 8923

8923 = 20000/(1+3e-k(4))     Yields  k = .2205934

 

At t= 8

f(t) =   20000/(1+3e-.2205934(8))      = 13213 people

 

 

When are 12192 infected?

12192 = 20000/(1+3e-.2205934t)       Solve for 't' weeks.....I'll let you finish     Hint :   should be less than the 8 weeks calc'd above !!

 Mar 25, 2020

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