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. a. How many times does this pattern need to continue until 100 000 teens know about the event?
7 years ago
Answered By Chris Y
You want to use exponential growth formula.AmountFinal=AmountInitial (growth rate)growth periodsThis question asks us to find the growth periods, "how many times does this pattern need to continue until 100000 teens know"Subbing in values to our equation we get something of the form:100,000 = 100 (4)p
we then divide each side by 100 to get1000 = 4p
take the log (base 10 of both sides)
log (1000) = p * log(4) [the p comes down is a property of logs]divide log(4) to get p by itself...log(1000)/log(4) = 4.98...
Checking our answer.100*45= 102,400 peoplenow the question seemed to impy that this pattern of teens telling four friends takes a week. In our case we need to round up to 5. Within 5 weeks if this pattern persisted 100k people would know.