Newton's law of cooling Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/differential-equations/newton-s-law-of-cooling/quiz/

1. 1

   dT/dt = −0.1(T − 20), T(0) = 90, find T(10)
   1. A) −457.5
   2. B) 45.75
   3. C) 90
   4. D) 33.11

2. 2

   dT/dt = −0.05(T − 20), T(0) = 100, find T(20)

   Answer: ____________________

3. 3

   dT/dt = −0.1(T − 22), T(0) = 72, find T(15)
   1. A) 72
   2. B) 16.07
   3. C) −331.6
   4. D) 33.16

4. 4

   dT/dt = −0.15(T − 20), T(0) = 80, find T(8)

   Answer: ____________________

5. 5

   dT/dt = −0.2(T − 25), T(0) = 95, when is T = 40
   1. A) t ≈ 77
   2. B) t ≈ 7.7
   3. C) t ≈ 95
   4. D) t ≈ −7.7

6. 6

   dT/dt = −k(T − 20), T(0) = 100, T(10) = 60, find T(20)

   Answer: ____________________

7. 7

   dT/dt = −0.05(T − 18), T(0) = 98, when is T = 38
   1. A) t ≈ 27.73
   2. B) t ≈ −27.73
   3. C) t ≈ 277.3
   4. D) t ≈ 98

8. 8

   dT/dt = −k(T − 20), T(0) = 5, T(10) = 12, find T(30)

   Answer: ____________________

9. 9

   dT/dt = −k(T − 70), T(0) = 350, T(10) = 250, find k
   1. A) k ≈ 0.0442
   2. B) k ≈ 350
   3. C) k ≈ −0.0442
   4. D) k ≈ 0.442

10. 10

    dT/dt = −0.25(T − 20), T(0) = 100, when is T = 30

    Answer: ____________________