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the preston curve shown below is an empirical cross-sectional relationship between life expectancy and real per capita income also known as gdp per capita it uses the function l of i equals 6.6354 times natural log i plus 10.754 to model the average life expectancy l of i given a countryamp;#39;s real per capita income i we want to use the function to answer the questions that follow but first notice how the relationship between the gdp per capita and life expectancy does appear to be logarithmic as shown here notice as the gdp per capita increases so does the life expectancy in most cases however notice how the increase in life expectancy is the greatest when the gdp per capita is between zero and ten thousand letamp;#39;s look at our first question we want to use the function l of i to estimate the average life expectancy in a country with a real per capita income or gdp per capita of five thousand dollars which means we want to evaluate l of five thousand so weamp;#39;ll substitu
