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5-57.

A weather balloon is launched and the following data is sent to the meteorological center. The column marked time, t, is given in seconds after launch, elevation, e, is in feet above sea level, and temperature, T, is in degrees Fahrenheit. Homework Help ✎

Time (t)

Elevation (e)

Temp (T)

0

1260

56.4°

30

1560

55.1°

60

1920

53.9°

90

2350

51.9°

120

2750

49.5°

150

3170

47.7°

180

3600

45.0°

210

4080

42.4°

240

4560

40.9°

  1. Approximately how fast is the balloon rising at 120 seconds?

    Since the derivative (IROC) cannot be determined, calculate the average rate of change.
    For e(t):

  2. Approximately how fast is the temperature changing at 2750 feet elevation?

    Use Hana, Anah, or Hanah's method to approximate the rate of change for T(e) at e = 2750.

  3. Approximately how fast is the temperature changing at 120 seconds?

    Use Hana, Anah, or Hanah's method to approximate the rate of change for T(t) at t = 120.

  4. Why would you expect the product of the answers to (a) and (b) to equal answer (c)?