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The function \[N(t)=\frac{ 300 }{ 1+299e ^{-0.36t} }\] describes the spread of a rumor among a group of people in an enclosed space. N represents the number of people who have heard the rumor, and t is measured in minutes since the rumor was started. Which of the following statements are true? Check all that apply.

AThere are 300 people in the enclosed space.
BIt will take 30 minutes for 100 people to hear the rumor.
CThe rate at which the rumor spreads speeds up over time.
DInitially, one person had heard the rumor.

Verified Answer :

nobillionaireNobley

There are 300 people in the enclosed space.


Initially, one person had heard the rumor.

Answer:

there are 300 people in the enclosed space

initially one person had heard the rumor.

Step-by-step explanation:

\(N(t)=\frac{300}{1+299e ^{-0.36t} }\)

Here top number represents the number people in the enclosed space

So,  there are 300 people in the enclosed space

t= 30 minutes

Plug in 30 for t then N(30) becomes

\(N(30)=\frac{300}{1+299e ^{-0.36*30}}=298\)

So second option is not correct

To find initial number of persons we plug in 0 for t

\(N(t)=\frac{300}{1+299e ^{-0.36*0}}\)

\(N(t)=\frac{300}{1+299*1}=1\)

So initially one person had heard the rumor.


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