There are 650,000 people in a city. Every 15 minutes, the local media broadcasts an important announcement about a huge downtown fire. During each 15 minute time period, 42% of the people who have not yet heard the news become aware of the fire. How many people have heard the news about the downtown fire after 1 hour? after 2 hours? I have trouble with creating formulas, and this is for my math practicum class, and we need to create a lesson plan around this problem. I first need help understanding the problem. 650,000 - 650,000(.42) 15 minutes 377,000- 377,000(.42) 30 minutes ... n-n(.42) I mean this is probably completely wrong, but I have trouble with creating these formulas. Thank YOU!!
If this helps I answered it as an exponential decay problem. Starting with 650000 people, the rate of decay is .42 (each time period 42% hear about it, and the decay rate is per time period, or 4 in an hour. y = a(1 - r)^t a = initial amount r = decay rate (1 - r) = decay factor t = time, or time since starting time So, the amount of people who have NOT heard the news after one hour is 650000(.58)^4. Or 650000 minus this for how many have heard.
Each 15 minute period, 42% of who is left hear about the fire. So after 15 minutes, that's 100% - 42% = 58% ? 650000. have still not heard So, in 30 minutes, 58% of the first 58% have still not heard. That's 0.58 (0.58 ? 650000), = 0.58^2 ? 650,000 right? After 45 minutes, 58% of 58% of 58% haven't heard, so 0.58(0.58(0.58 ? 650,000)) = 0.58^3 ? 650,000 So following this pattern, after n multiples of 15 minutes, there would be 0.58^n ? 650,000 who still have not heard. So if t = the number of minutes, and p = people who have not heard, you'd have p = 0.58 ^ (t/15) ? 650,000 So if you want to know how many people HAVE heard, what final step would you do? That's what I would say anyway, see if you agree.