**
**##

## Activity 5:

## Expressing Rules for Atmospheric Pressure

**Directions: **Solve the exponential equations given below to compute various
atmospheric pressures.

**Introduction**

The early work that led to our understanding of the planetary motions and gave
us the description of the solar system we know today would have been virtually
impossible without the use of logarithms to reduce the labor of computations.
Although computers and calculators have replaced logarithms as computational
tools, logarithmic and exponential functions are still essential for the study
of Earth's atmosphere and rocket propulsion.

**Problem 1**

Experimentation and theory have shown that an approximate rule for atmospheric
pressure at altitudes less than 80 km is the following: Standard atmospheric
pressure,1035 grams per square centimeter, is halved for each 5.8 km of vertical
ascent.

A) Write a simple exponential equation to express this rule.

B) Compute the atmospheric pressure at an altitude of 40 km.

C) Find the altitude at which the pressure is 20%of standard atmospheric pressure.

**Directions:** Solve the exponential equations given below to compute various
atmospheric pressures.

**Problem 2**

The rule for the variation of atmospheric pressure with height can be written:

P =1035 (2)^{Ðh/5.8}

P =1035 (2)^{Ð0.17h}

Atmospheric scientists often use this rule in one of its equivalent forms
where the base is 10 or e, the base of the natural logarithms, instead
of 2.

Find k_{1} and k_{2} so that P =1035 (2) ^{Ð0.17h}
=1035 (10)^{Ðk 1 h} =1035 (e )^{Ðk 2 h}