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3) (6 pt) Average growth rate The ination-adjusted S&P 500 stock index was equal to 3 at the end of 1947, and it was equal to 150 - S at the end of 2017. a) What is the average growth rate of the S&P 500 index between 1947 and 2017? Express your answer in percent per year (Hint: Use the formula for the average growth rate. If X, is a function of time, its average growth rate between dates t = a andtzb, b>a, is _ 1n Xb 1n X, g b a ' Your answer should not depend on the numerical value of S). b) Given the data above, how many years, on average, does it take for the S&P 500 index to double? c) Between 1967 and 2017, US real GDP (Y) grew at an average annual rate of 2.75%, and real expenditure on health care (X) grew at an average annual rate of 5.5%. In 1967, 4.5% of GDP was spent on health care, that is, g- = 0.045. Assuming the same average growth rates apply in the future as well, calculate the percentage of GDP spent on health care in 2037, that is, calculate Xi\". 1'2037 .\\ 1 H - n A' , a. 1