The Gompertz Equation; Learning Curves The concept of learning curves has broad application in business, medicine, and many other fields. For example, the Gompertz equation is a mathematical model that can be used to predict the number of deaths at a certain age. The Gompertzequation is very similar in form to that of the learning curve, except that e, the base of the naturallogarithm, is used and there is a positive rather than a negative exponent in the equation. When usedto predict death rates, the Gompertz equation is as follows:M(x) = AeGxwhereM(x) = the number of deaths in a population of 100,000 of those at age x; M(x) is often calledthe mortality rateA = the initial mortality rate at age 0G = the exponential rate of increase in mortality for an increase in age, xe = a mathematical constant, the base of the natural logarithm, which equals approximately2.718281828In this context, the Gompertz equation is used to estimate the number of deaths at a given age. Theequation was estimated using nonlinear regression based on 2002 U.S. census data, and the following estimated equation was derived (for ages 25 through 90). The regression had a very good fit,with an R-squared of 0.97:M(x) = 8.84e.08xRequired1. Use the exponential function on your calculator or the EXP function in Excel to determine the mortalityrate of any age you choose between 25 and 90.2. Think of an application or two for which an exponential equation like the Gompertz equation could beused in cost estimation
The Gompertz Equation; Learning Curves The concept of learning curves has broad application in business, medicine, and many other fields. For example, the Gompertz equation is a mathematical model that can be 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. When used
to predict death rates, 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
In this context, 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 through 90). The regression had a very good fit,
with an R-squared of 0.97:
M(x) = 8.84e.08x
Required
1. Use the exponential
rate of any age you choose between 25 and 90.
2. Think of an application or two for which an exponential equation like the Gompertz equation could be
used in cost estimation
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