Answer to Question #121909 in Algebra for queen

Question

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 musician’s website, 100 teens in the area will find out about the event in the first week. Research suggests that each of those teens will tell four new teens about the event, and those friends each will tell four more teens about it. How many times does this pattern need to continue until 100 000 teens know about the event?

Answer 1

After the first week, 100 teens will know about this concert. After the second week, the number of new teens will be 400, as each of the 100 original teens will tell four of their friends. After the third week, new teens will be 1600, as 400 teens told their friends. And so on, the number of new teens will be multiplied by 4 for every week.

100 -> 100+400=500 -> 100+400+1600=2100 -> 100+400+1600+6400=8500 -> 100+400+1600+6400+25600=34100 -> 100+400+1600+6400+25600+102400=136500

Answer: 6 weeks