Question

9. A concert hall is filling with people from noon until show time at 3:00 pm. The table below shows the rate of people entering the concert hall (measured in people per minute) at particular times. Time Noon 1:00 1:30 2:00 2:20 2:40 2:55 2:50 3:00 8 11 14 17 21 23 26 25 Rate (people per min) a)Estimate the total number of people attending the show using a midpoint approximation for four partitions: [noon, 1:30]. [1:30,2:20], [2:20,2:50], and [2:50,3:00] in terms of minutes. 11(10%)e-001 b) One possible model for the rate at which people enter the concert hall is given by the function R(t) = (1 +1600e -0.01)2 people per minute, where t is the time in minutes since noon. Write and evaluate (rounded to the nearest person) an expression that represents the total number of people at the concert hall at 3pm, as predicted by this model

Answer 1

9. A concert hall is filling with people from noon until show time at 3:00 pm. The table below shows the rate of people entering the concert hall (measured in people per minute) at particular times. Time Noon 1:00 1:30 2:00 2:20 2:40 2:50 2:55 3:00 4 8 11 14 17 21 23 26 25 Rate (people per min) a)Estimate the total number of people attending the show using a midpoint approximation for four partitions: (noon 1:30],[1:30 2:20], [2:20, 2:50], and [2:50,3:00] in terms of minutes, 4 Sum using mid-poinst oule = ² R(K). Ak kal x 90+14 x 50+21x30 +26*/0 = 720+ 700+630+260 2310 b) One possible model for the rate at which people enter the concert hall is given by 11(10%-0.011 the function R(t) = (I +1600e -0012 people per minute, where t is the time in minutes since noon. Write and evaluate (rounded to the nearest person) an expression that represents the total number of people at the concert hall at 3pm, as predicted by this model According to the given model we have 180 11(106)e-0.017 dt [3 hours = 3 x 60 minutes = 180 minutes] (1 1 + 1600e -0.011)2 =11. 106-1100 e-0.011 (1 +16002 -0.018) 2dt 180 = 11000000 e-0.011 (1 + 16000 -0.011 2 265.47822 = 11000000 - 5,265, 1 164 du Apply u- substitution:u=1+1600e -0.017 16 = 11000000 ( - 265.4782 = 11000000(-( 1262 1-4-1 J265.47822 u-?eiu)) = 11000000 ,-2+1 1601 - 2+1 .265.47822 = 6375006 – – 265.4782... = 687500 0.00314... = 2160.24717 So rounded number to nearest whole number = 2160