SOLUTION: Initially, 10 students at Kampung Tembikai contracted influenza. The flu spread
over time and the total number of students who eventually contracted the flu
approached but never
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over time and the total number of students who eventually contracted the flu
approached but never
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Question 1171737: Initially, 10 students at Kampung Tembikai contracted influenza. The flu spread
over time and the total number of students who eventually contracted the flu
approached but never exceeded 200. Let P(𝑡) denote the number of students who
had contracted the flu after 𝑡 days, where P is an appropriate function.
Sketch the graph of P and indicate where the function is increasing by showing the
interval. If the horizontal asymptote exists, what would the line be? Discuss the
concavity of the graph by explaining its significance. Identify the inflection point and
explain why it exist. Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! P(t)=L/(1+Be^-(kt))
when t=0, P(t)=10
The denominator is 1+B, and L/(1+B)=10
L=10+10B
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L=200, the horizontal asymptote. When k is large, Be^-(kt) becomes close to 0 and the denominator 1.
Since L=10+10B, B=19
P(t)=200/(1+19 e^(-kt))
The inflection point is where the 2nd derivative goes from positive to negative and is at L/2 or 100 cases.
The horizontal asymptote is at P(t)=200.
