Question 279263: AT 8AM 7 PEOPLE HAVE HEARD A RUMOR. AT 11AM 75 PEOPLE HAVE HEARD THE SAME RUMOR. LET F(T) REPRESENT THE NUMBER OF PEOPLE WHO HAVE HEARD THE RUMOR T HOURS AFTER 6AM AND ASSUME THAT THE NUMBER OF PEOPLE IS GROWING EXPONENTIALLY. FIND AN EQUATION FOR F(T), AT WHAT RATE IS THE RUMOR SPREADING, DETERMINE THE TIME IT TAKES FOR 1500 PEOPLE TO HEAR THE RUMOR.
Found 2 solutions by CharlesG2, stanbon:
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! AT 8AM 7 PEOPLE HAVE HEARD A RUMOR. AT 11AM 75 PEOPLE HAVE HEARD THE SAME RUMOR. LET F(T) REPRESENT THE NUMBER OF PEOPLE WHO HAVE HEARD THE RUMOR T HOURS AFTER 6AM AND ASSUME THAT THE NUMBER OF PEOPLE IS GROWING EXPONENTIALLY. FIND AN EQUATION FOR F(T), AT WHAT RATE IS THE RUMOR SPREADING, DETERMINE THE TIME IT TAKES FOR 1500 PEOPLE TO HEAR THE RUMOR.
kindly repost without shouting, check you posted problem correctly, and be patient for an answer, thank you
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! AT 8AM 7 PEOPLE HAVE HEARD A RUMOR. AT 11AM 75 PEOPLE HAVE HEARD THE SAME RUMOR. LET F(T) REPRESENT THE NUMBER OF PEOPLE WHO HAVE HEARD THE RUMOR T HOURS AFTER 6AM AND ASSUME THAT THE NUMBER OF PEOPLE IS GROWING EXPONENTIALLY. FIND AN EQUATION FOR F(T), AT WHAT RATE IS THE RUMOR SPREADING, DETERMINE THE TIME IT TAKES FOR 1500 PEOPLE TO HEAR THE RUMOR.
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i am assuming that the rumor started at 6am and by 8am only 7 people had heard the rumor.
0::::::1 person
2::::::7 people
5::::::75
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If the relation is exponential, the least-squares regression
equation is
F(T) = 1.09(2.3578)^x
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The the time (x) for 1500 people results from
solving 1.09(2.3578)^x = 1500
2.3578^x = 1376.15
x = log(1376.15)/log(2.3578)
x = 8.4257 hours
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Time would be 6AM + 8.4257 hrs
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cheers,
Stan H.
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