Evaluating and Solving Logarithmic Functions
The Preston curve (Shown below) is an empirical cross-sectional relationship between life expectancy and real per capita income (GDP per capita). It uses the function $\displaystyle {L}{\left({i}\right)}={6.6354}\cdot{{\log}_{{2.72}}{\left({i}\right)}}+{10.754}$ to model the average life expectancy $\displaystyle {L}{\left({i}\right)}$ given a countries real per capita income (GDP per capita) $\displaystyle {i}$. Use this function to answer the questions that follow.
Preston Curve $\displaystyle {L}{\left({i}\right)}={6.6354}\cdot{{\log}_{{2.72}}{\left({i}\right)}}+{10.754}$
Use the function $\displaystyle {L}{\left({i}\right)}$ to estimate the average life expectancy in a country with a real per capita income (GDP per capita) of $5,500. Round your answer to two decimal places $\displaystyle {L}{\left({5500}\right)}=$ In a country with a real per capita income (GDP per capita) of $5,500, the average life expectancy is years.
Use the function $\displaystyle {L}{\left({i}\right)}$ to estimate the real per capita income (GDP per capita) in a country whose average life expectancy is 67 years. Round your answer to two decimal places $\displaystyle {L}{\left({i}\right)}={67}$ when $\displaystyle {i}=$ In a country with an average life expectancy of 67 years, the real per capita income (GDP per capita) is estimated to be $.

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