How Many People Become Ill with the Flu During the First 10 Days of an Epidemic?

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SUMMARY

The rate at which individuals become ill with the flu during the initial 10 days of an epidemic is modeled by the equation r = 1000t e^(-t/20). To determine the total number of people who become ill in this period, one must compute the definite integral of this function from 0 to 10 days. The calculated result of this integral is 36,081, confirming that the approximation is accurate given the continuous nature of the function versus the discrete count of individuals.

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helpm3pl3ase
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Is this correct??

The rate r at which people become ill with the flu at time t days after
an epidemic begins is given by r = 1000 t e−t/20 people per day. How many
people become ill with the flu during the first 10 days of this epidemic?

take the integral from 0 to 10 of (1000t e^(-t/20)) and then plug in 10 and 0. Then subtract.. getting

36081
 
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Yes, assuming the information given is what you have said, that's correct. (More correctly,since the function you give is continuous while the number of people is discrete, its the "best approximation".)
 

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