number ' (t) = 100e^t + 75t
number (t) = 100e^t + (75/2)t^2 + c
assuming at opening (t=0) no people were in the zoo,
0 = 100e^0 + (75/2)(0) + c
c = -100
number(t) = 100e^t +(75/2)t^2 - 100
so when t = 2.666.. (at 9:40 am)
number(2.666...) = 100e^2.6667 + 37.5(2.666..) - 100
= appr 1439 hundreds
Looks like way to many people in a zoo
People are entering a zoo at the rate of 100e^t+75t people per hour where t is the amount of time the zoo has been open on that day measured in hours. If the doors are open at 9:00 AM, how many hundreds of people have entered the zoo at 11:40 AM? (Nearest integer)
1 answer