The concept of learning curves has broad application in business, medicine, and many other fields. For example, the Gompertz equation is a mathematical model used to predict the number of deaths at a certain age. The Gompertz equation is very similar in form to that of the learning curve, except that e, the base of the natural logarithm, is used and there is a positive rather than a negative exponent in the equation. The Gompertz equation is as follows:

M(x) = AeGx

Where:

M (x) = the number of deaths in a population of 100,000 of those at age x; M ( x ) is often called the mortality rate.

A = the initial mortality rate at age 0.

G = the exponential rate of increase in mortality for an increase in age, x.

e = a mathematical constant, the base of the natural logarithm, which equals approximately 2.718281828.

The Gompertz equation is used to estimate the number of deaths at a given age. The equation was estimated using nonlinear regression based on 2002 U.S. census data and the following estimated equation was derived (for ages 25–90). The regression had a very good fit, R - squared of 0.97.

M(x) = 8.84e.08x

Required

1. Use the exponential function on your calculator or the EXP function in Excel to determine the mortality rate of any age you choose between 25 and 90.

2. Think of an application or two that an exponential equation like the Gompertz equation could be used in cost estimation.