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.

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

@DemolisionWolf I know we just did one like this but could you help me figure this one out? I think that D is a correct answer, but I don't know about the rest

shamil98 · Answer

I'm doing the same one haha

anonymous · Answer

no way! hahah let me know if you figure anything out :p

shamil98 · Answer

alright, prob not tho I barely understand this stuff lol

anonymous · Answer

me too D:

anonymous · Answer

hey, you still looking for help?

anonymous · Answer

thank you so much, but not at the moment, i have to go to sleep since im waking up early tomorrow, thank you again though! :)

anonymous · Answer

yep

anonymous · Answer

$$N=\frac {300} {1+299e^{-0.36t}}$$
'[N=\frac {300} {1+299e^{-0.36t}}\]

Part A-
when there is an exponential equation like this where its in the denominator and the neumerator is a constant. the neumerator constant is the 'cap' or the 'max' remember in the other problem where we had the population of people, and it's cap was 64billion, this is the same idea. so 300 is a 'cap' 

Part B-
30 minutes for 100 people to hear the rumor. So, plug in t=30 into the equation. If it equals 100 then this statement is true.

Part C- "The rate at which the rumor spreads speeds up over time."
for this part, i'm not sure how to answer T/F for this... It's asking for a value from what I can tell.

Part D - "Initially, one person had heard the rumor."
this one means that N=1, so you'll have to plug in 1 for n, and solve the equation in reverse to find what t would equal. remember that t is minutes. so if you get a negative t, then you'll know this statement is false.