The function
N(t)=3001+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.

A. There are 300 people in the enclosed space.
B. It will take 30 minutes for 100 people to hear the rumor.
C. The rate at which the rumor spreads speeds up over time.
D. Initially, one person had heard the rumor.

Question

The function 
N(t)=3001+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.

A. There are 300 people in the enclosed space.
B. It will take 30 minutes for 100 people to hear the rumor.
C. The rate at which the rumor spreads speeds up over time.
D. Initially, one person had heard the rumor.

anonymous · Answer

ok the equation got messed up need to fix it

anonymous · Answer

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

anonymous · Answer

the only one i am positive is A

anonymous · Answer

@tkhunny @shamim @Destinymasha @jim_thompson5910 @thomaster @kropot72 MInd helping me with this problem n_n ?

miracrown · Answer

Ok - Let's check part A.
If we evaluate N(t) when t = 0 we get:

|dw:1402626472219:dw|

So A is true - there are 300 people in the enclosed space.
And given enough time, everyone will learn of the rumor.