Question

The function N(t)=300/(1+299e^-0.36t) describes the spread of a rumor among a group 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?
a. The rate at which the rumor spreads speeds up over time.
b. Initially, only one person had heard the rumor.
c. It will take approx. 14 mins for 100 people to hear the rumor.
d. There are 299 people in the enclosed space.

Answer 1

A ) The rate at which rumor spreads speed up over time. If t increases, also N(t) increases, because 300 is divided by the smaller number.( Correct )B ) 1 = 300 / ( 1 + 299 · e^(-0.36 · 0 ) ) 1 = 300 / ( 1 + 299 · 1 ) 1 = 300 / 3001 = 1  ( Correct )C ) 100 = 300 / ( 1 + 299 · e^(-0.36 · 14 ) )100 = 300 / ( 1 + 299 · 1/154.47 )100 = 300 / 2.93565100 ≈ 102.192        ( Correct ) - approx. 14 minutes
D ) N = 300 / ( 1 + 299 · e^(-∞) )N = 300 / ( 1 + 299 · 0 ) N = 300 / 1 = 300299 people are enclosed space ( Not correct )Answer:True statements are: A ) ,  B )  and  C ) .