Download Slide 1 - Beachwood City Schools

Part (a)
To find the total number of cars,
we need to integrate.
# of cars =
30
(82 + 4 sin(t/2)) dt
2474.077
0
Keep in mind that you
must be in RADIANS.
2474 cars
Part (b)
Since F(t) is the traffic flow, then F’(t) would be the
RATE OF CHANGE of the traffic flow.
We were asked if the traffic flow was increasing or
decreasing at t=7. For this, we’ll need the derivative.
F’(t) = 2 cos (t/2)
-1.872 or -1.873
Since F’(7) is negative, the
traffic flow is decreasing at t=7.
Part (c)
NOTE: Part (c) uses a formula from
Calculus, while Part (d) is nothing more than
an Algebra 1 problem.
The AP Test graders don’t expect you to show the
work for this integration (u-subs, etc). That just
wastes your valuable testing time. Instead, simply
show them your integral and then evaluate it using
15
1
the
graphing
calculator.
Average value =
(82 + 4 sin(t/2)) dt
15-10
10
Average value = 81.899 cars/minute
Part (d)
The AVERAGE RATE OF CHANGE is not Calculus.
It’s the slope formula from Algebra 1.
Keep in mind that you
must be in RADIANS.
AVG. RATE
=
OF CHANGE
F(15) – F(10)
85.752 – 78.164
15 - 10
15 - 10
1.517 or 1.518 cars/min2