PLEASE HELP, I'M VERY CONFUSED!

[math-a-phobic]

Hi, I am lost and don't know how to solve this problem. :? Please explain how I would go about solving this problem and thank you for your assistance.

Problem: The rumor that there would be a party on the last Friday of each month spread throughout Lake View Academy. The student who started the rumor told four students the first hour. Every hour each person who knew the rumor told four different student who did not yet know it. Find a pattern and express it in words. Afterwards, express the pattern mathematically. What is the radical function for this problem? Its asymptotes? How long did it take before all 625 students had heard the rumor?

 

[Denis]

Not too important, but if there are 625 students, then question should be:
"How long did it take before all remaining 624 students had heard the rumor?"
....why? Because one student started the rumor!

(1)4[4], (2)16[20], (3)64[84], * (4)256[340], (5)1024[1364]

*340 had heard it after 4 hours; so took 4 hours and a few minutes...all yours :wink:

 

[soroban]

Hello, math-a-phobic!

What did you try? . . . anything?
Or are you just waiting for a Magic Formula?

The rumor that there would be a party on the last Friday of each month spread throughout Lake View Academy.
The student who started the rumor told four students the first hour.
Every hour each person who knew the rumor told four different student who did not yet know it.
Find a pattern and express it in words.
Afterwards, express the pattern mathematically.
What is the radical function for this problem? Its asymptotes? . . . radical? asymptotes?
How long did it take before all 625 students had heard the rumor?

How about Thinking?

At \(\displaystyle t\,=\,0\), only that one student had "heard" the rumor: 1

At \(\displaystyle t\,=\,1\), he told 4 other students . . . There are now 5 students who've heard the rumor.

At \(\displaystyle t\,=\,2\), each of these 5 students told 4 others: 20 more students . . . There are now: \(\displaystyle \,5\,+\,20\:=\:\)25

At \(\displaystyle t\,=\,3\), each of the 25 students told 4 others: 100 more students . . . There are now: \(\displaystyle \,25\,+\,100\:=\:\)125

At \(\displaystyle t\,=\,4\), each of the 125 students told 4 others: 500 more . . . There are now: \(\displaystyle \,125\,+\,500\:=\:\)625

Well, that answers one question . . . 4 hours.


Do you recognize that the numbers are power-of-5? \(\displaystyle \:5,\:5^2,\:5^3,\:5^4\)

In general, after \(\displaystyle n\) hours, the number of students is: \(\displaystyle \,5^n\)

[It has no radicals and no asymptotes. \(\displaystyle \;\)What were they thinking?]

 

[math-a-phobic]

Hi Denis and Soroban, thanks for your help. I did try guessing and checking equations, but I think there is a formula. I just don't know how to get it. :? Thanks again for your help. I really appreciate it.