### Home > APCALC > Chapter 5 > Lesson 5.2.1 > Problem5-57

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?

$\text{You can use Hana's method: }\frac{e(150)-e(120)}{150-120}$

$\text{or Anah's method: }\frac{e(120)-e(90)}{120-90}$

$\text{or Hanah's method: }\frac{e(150)-e(90)}{150-90}$

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)?

$\text{Rewrite: }e'(t)=\frac{de}{dt} \text{ and }T'(e)=\frac{dT}{de}$

$\frac{de}{dt}\cdot \frac{dT}{de}=$