5 Steps to a 5 AP Calculus BC 2019

398 STEP 5. Build Your Test-Taking Confidence

Section II Part A

1. (A) At 1:00 a.m.,t=6.
   f(6)= 96 −20 sin

(

6

4

)

= 76. 05 ◦≈ 76 ◦Fahrenheit

(B) Average temperature

=

1

12

∫ 12

0

[

96 −20 sin

(

t

4

)]

dt.

Using your calculator, you have:

Average temperature=

1

12

(992.80)

= 82. 73 ≈ 82. 7.

(C) Lety 1 = f(x)= 96 −20 sin

(

x

4

)

and

y 2 = 80.

Using the [Intersection] function of your

calculator, you obtain

x= 3. 70 ≈ 3 .7orx= 8. 85 ≈ 8. 9.

Thus, the heating system is turned on

when 3. 7 <t< 8 .9.

[−2,10] by [−10,100]

(D) Total cost

=(0.25)

∫ 8. 9

3. 7

(80−f(t))dt

=(0.25)

∫ 8. 9

3. 7

[

80 −

(

96 −20 sin

(

t

4

))]

dt

=(0.25)

∫ 8. 9

3. 7

(

− 16 +20 sin

(

t

4

))

dt.

Using your calculator, you have:

=(0.25)(13.629)= 3. 407

≈3 dollars.