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 the 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, examples of which are cited in this chapter.

**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.