Question 173277
The numbe of people who hear a rumor increases exponentially. If 20 people start a rumor and if each person who hears the rumor repeats it to two people a day, the number of people N who have heard the rumor after t days is given by the function N(t) = 20(3)^t
a. How many people have heard the rumor after 5 days?
N(5) = 20*3^5 = 4860
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b. After what amount of time will 1000 people have heard the rumor?
1000=20*3^t
50 = 3^t
tlog(3) = log50
t = log(50)/log(30
t = 3.56 days
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c. What is the doubling time for the number of people who have heard the rumor?
N(t) = 20*3^t
40 = 20*3^t
2 = 3^t
tlog(3) = log(2)

t = log(2)/log(3)
t = 0.631 days
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Cheers,
Stan H.