MATH 1306 – Homework Handout # 4

Answers To Selected Odd-numbered Problems

1b.       slope of tangent line m ≈ 1.42 (Answers may vary somewhat from person to person.)

1c.       1.42 is the instantaneous rate of change of C at t = 16 (Your answer should be the same as your answer to part 1b.)

1d.       At 4 pm (t=16), the number of cars on the expressway is increasing by 1.42 thousand cars per hour, on a typical weekday.

1e.       C '(17) = 0

3b.        slope of the tangent line m ≈ 3.5 (Answers may vary somewhat from person to person.)

3c.        3.5 is the instantaneous rate of change of I at t=14 (Your answer should be the same as your answer to part 3b.)

3d.        At 2 pm on a recent trading day, the NASDAQ was increasing by 3.5 points per hour.

3e.        I '(11) = 0

5b.        slope of tangent line m ≈ 16.3 (Answers may vary somewhat from person to person.)

5c.        16.3 is the instantaneous rate of change of T at the input m = 8

5d.        After 8 minutes of working out on the cross trainer machine, the total calories burned by Imani is increasing by 16.3 calories per minute.

5e.        T '(8) = 16.3

7a.        For a typical 40 year old American, the daily amount of time watching TV is decreasing by 0.025 hours per year. [0.025 hr = 1.5 min]

9a.       S(0)=42; In 1990, the number of persons receiving Social Security benefits was predicted to be 42 million.

9c.        slope of tangent line m ≈ 0.425

9d.        S '(40)≈0.425; This is because S '(40) equals the slope of the tangent line at the input 40.

9e.        In 2030 (t=40), the number of persons predicted to be receiving Social Security benefits is increasing by 0.425 million per year (or 425,000

             per year).