00:01
Question, they said that the rate at which cars enter a parking lot is modeled by this function e of t, which is 30 plus 5 times the quantity of t minus 2 times the quantity of t minus 5 times e to the power of negative 0 .2 t.
00:17
I'm not going to need l for this question, but e of t is measured in cars per hour, and time is measured after 5 a .m.
00:25
Defined from times 0 to to 12.
00:28
For times 0 through 6, $5 are collected from each car entering the parking lot.
00:34
For times 6 through 12, $8 are collected from each car entering the parking lot.
00:41
I want to know how many dollars are collected from the cars entering the parking lot from time t equals 0 to time t equals 12, giving our answer to the nearest whole dollar.
00:55
So what are we going to do? well, e of t is the rate that cars enter the parking lot.
01:03
So to figure out how many cars enter the parking lot from time 0 to 6, we are going to compute the integral from 0 to 6 of e of t dt.
01:16
Then to get how much money was collected over that time interval, i must multiply by 5.
01:23
To that, i'm going to add.
01:25
Now from time 6 to 12, how many cars enter the parking lot? well, that would be the integral from 6 to 12 of e of tdt.
01:38
I'm going to multiply that by 8...