SOLUTION: 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 peopl

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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?
b. After what amount of time will 1000 people have heard the rumor?
c. What is the doubling time for the number of people who have heard the rumor?

Answer by stanbon(75887) About Me  (Show Source):
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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.