Calculus Question

Question

The function below represents the number of people who have a rumor t hours after it has started.

N(t)=500/1+499e^−0.3t.

(You may wish to sketch a graph of N(t) to help you understand this situation and answer the questions below.) 

For part (b), round your answers to the nearest whole number. 

(a) What is N(0)?  

 Consider what significance this has.  

(b) How many people will have heard the rumor after 2 hours? 

 

After 11 hours?  

 

(c) When will half the people have heard the rumor? t=

(d) When is the rumor spreading fastest? t= 

Answer 1

N(t)=500/(1+499e^−0.3t)

N(0) = 1 The significance is that only person hears the rumor because this person started it...

(b) How many people will have heard the rumor after 2 hours?  rounds up to 2 people

 

After 11 hours?  rounds up to 26

 

(c) When will half the people have heard the rumor? t= 21 hours, it rounds up to 260 people

(d) When is the rumor spreading fastest? approximately between 15 and 26 hours.

My recommendation on these type of problems, graph it. Visual understanding increases your ability to understand the mathematical slope implications