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

1. Approximately how fast (in ft/sec) is the balloon rising at $120$ seconds?

   Steps (a):

   Since we cannot find the derivative (IROC), calculate the average rate of change.
   For $e(t)$:
   You could use Hana’s method: $\frac{e(150)-e(120)}{150-120}$
   or Anah’s method: $\frac{e(120)-e(90)}{120-90}$
   or Hanah’s method: $\frac{e(150)-e(90)}{150-90}$

2. Approximately how fast is the temperature changing (in °F/ft) at $2750$ feet?

   Hint (b):

   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 (in °F/sec) at $120$ seconds?

   Hint (c):

   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)?

   Hint (d):

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