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

te midpoint Rule: Given, until show from noon Rate of filing with peoples time at 3:00 pm 1:30 9:20 1:00 2:00 Noon 240/3:50 3:553.00 Time 93 17 11 8 Rate (people per min) e, we have to estimate the total number of people attending the show using mid point approximation for your paritions Given intervals are in clock time so change it into minutes since noon as follows: [0,90],[90,140],[140,170],[170,180] Length of each interval Therefore, by the midpoint Ruie: is 90, 50, 30,10 Number of peoples : 8790+ 1050+ 01* 30+36x18 : +20+ 700+ 630+ 260 2310 Hence, the required number are 2310, of peoples

enter is given var at which peorie by possible michiel for the au follows: R(He 111106)e-0.01t L ( 1+1600 -0.014) we have to find total number of peoples at 3pm. Using given models From noon to 3pm it is shoors that it 180 minutes so integrate the given model from oto 180 we get 0.01772014 -0.017 به oH 6 -Ilx10 180 -0.014 Number of peoples J (106) ö (11600 e : 11x106 16001-0.012 (Soo-ool) 0 P1+1600 -0.012 180 ((+ 16000 .-0011 1600(-0.01) -118 106 1600 (-0.01) [11 +1600 2-0.014) Jo - 2160 Hence, the required numbers of peoples are 2160, वी 7180
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