To find the rate of change, we must find the amount of people that have changed over a given time period, and then find the unit rate. As 473-23=450 (we can subtract because we have the end number minus the starting number to find the amount changed) students enter over 10 minutes, and we want to find the rate of change for 1 minute, we can divide 450 10 times. As we move the decimal point of a number 1 to the left when dividing by 10, we have 450.00 -> 45.000 after dividing by 10. Therefore, the average rate of change is 45 students per minute. To find how many students will be in the auditorium after 15 minutes of filling, we can use this average rate of change to figure out approximately how many students will enter in 5 minutes. Therefore, as 45 students come in every minute, after 1 minute, 45 more students will come in. After 2, 45+45=45*2=90 students will come in, and so on. Thus, 45*5=225 students will come in after 5 minutes. Since we know that 473 students are in the auditorium after 10 minutes, we can add 225 to 473 to get 698 students after 15 minutes.
Feel free to ask further questions, and Happy Holidays!
