Question

The graph to the attached represents the rate at which people arrive at an amusement park ride throughout he day, where t is measured in hours from the time the ride begins operation. If there were 275 people in line when the ride began operation, How many people have waited in line for the ride after 4 hours?

Answer 1

@vishweshshrimali5 @SolomonZelman

Answer 2

Am I just finding the area under the curve from 0 to 4 hours? My answer is 4075 but I am not sure how they did it

Answer 3

maybe my brain is off right now, but doesn't it say straight out, (4,400) ?

Answer 4

the point (4,400) is there but this is how many people waited in line for a ride?

Answer 5

I don't know

Answer 6

yes, how many people waited in a line (for a ride), so 400ppl.
+ the 275 people that were waiting before anything started.

(I think....)

Answer 7

but my answer is suppose to be 4075

Answer 8

why ?

Answer 9

@helder_edwin

Answer 10

@jim_thompson5910 This is a calculus ap problem

Answer 11

the area under the curve represents the CHANGE in riders over the 4 hours (dy/dx represents the rate of change, dy is the change in riders over change in time dx)

The area under the curve is 3800 (see attached)

Answer 12

So that means an additional 3800 people have waited in line (from t = 0 to t = 4)

add this to 275 to get 275+3800 = 4075

Answer 13

ok now I see, Thanks

Answer 14

we add to 275 to account for the people already there

Answer 15

np

Answer 16

the curve itself is the derivative of the function that "counts" the number of people.