A special event organizer wants to get the word out to 100,000 teens in the area about a concert coming up in three months. By posting the event on the musicians' website, 100 teens in the area will find out about the event in the first week. Research suggests that each of those teams will tell for new teens about the event, in those friends each hotel for more teens about it.
a.) how many times does this pattern need to continue until 100,000 teens know about the event?
b.) what assumption is made in order to answer part a?
4 years ago
Answered By Rohtaz S
As specified, 100 teens will come to know about the event in one week and they tell 4 new teens about it.
Lets assume that all the teens will tell that information to 4 NEW TEENS only and the information does not travel backwards or sideways, basically assume that all the group sets are mutually exclusive.
Lets start now
Given: Our first group is 100 Teens, lets call it Group AThey will tell 4 person each, this implies 400 more teens will know about this event now, lets call it Group B and so on....
Group A =100 Group B =100 * 4 = 400Group C =400 * 4 = 1600Group D =1600 * 4 = 6400Group E = 6400 * 4 = 25600Group F = 25600 * 4 = 102400
So based on the pattern above, we can find how many teens know about the event. See below
500 2100 8500 34100 136500after
4 years ago
Answered By Rohtaz S
As specified, 100 teens will come to know about the event in one week and they tell 4 new teens about it.
Lets assume that all the teens will tell that information to 4 NEW TEENS only and the information does not travel backwards or sideways, basically assume that all the group sets are mutually exclusive.
Lets start now
Given: Our first group is 100 Teens, lets call it Group AThey will tell 4 person each, this implies 400 more teens will know about this event now, lets call it Group B and so on....
Group A =100 Group B =100 * 4 = 400Group C =400 * 4 = 1600Group D =1600 * 4 = 6400Group E = 6400 * 4 = 25600Group F = 25600 * 4 = 102400
So based on the pattern above, we can find how many teens know about the event. See below
1st Iteration = 500 Teens = Group A + Group B2ns Iteration = 2100 Teens = Group A + Group B + Group C3rd Iteration =8500 Teens = Group A + Group B + Group C + Group D4th Iteration =34100 Teens = Group A + Group B + Group C + Group D + Group E5th Iteration =136500 Teens = Group A + Group B + Group C + Group D + Group E + Group F
So, after 5th Ineration, more than 100000 teens will know about the event. This pattern reaches the target of 100000 sometime in between the 4th iteration and 5th iteration (before 5th one is completed).
4 years ago
Answered By Aleksandar B
Using the geometric formula Sn= a+ ar+ ar2+••••+arn-2+arn-1+arn=a(1-rn)/1-r we know that a=100 and r=4. We want to to find n so that Sn=100,000. This can be used to answer part a).
Plugging into the equation we have 100+400+1600+6400+25600+102400=136500. This pattern will continue 6 times so that there will be more than 100,000 teens.
Also solving for n, we have rn= 1-(1-r)(Sn)/a which translates to 4n=1-(-3)(1000)=3001. Taking log of both sides we get n=(log3001)/log4=5.7756.