Precal

The number of people in a town of 10,000 who have heard a rumor started by a small group of people is given by the following function:

N(t) = 10,000/(5 + 1245e-.97t)

14. How many people were in the group that started the rumor?

15. How many people have heard the rumor after 1 day? After 5 days?

16. How long before 1000 of the people in the town have heard the rumor?

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  1. #14. well, e^0 = 1, so N(0) = 10000/1250

    #15. Just plug in 1 or 5 for t and crank it out.

    #16 just solve for t in

    10,000/(5 + 1245e-.97t) = 1000
    5 + 1245e-.97t = 10
    1245e^-.97t = 5
    e^-.97t = 5/1245
    -.97t = ln(5/1245) = -5.517
    t = 5.68 days

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