Total personal income of the country (in billions of dollars) for selected years from 1956 to 2001 is given in the table. (a) These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years after 19 (b) If this model is accurate, what will be the country's total personal income in 2006? (c) In what year does the model predict the total personal income will reach $23 trillion?

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Year
1956
1966
1976
1986
1996
2001
Personal Income
414.6
836.7
2313.1
4883.4
8428.7
10,234.4
Transcribed Image Text:Year 1956 1966 1976 1986 1996 2001 Personal Income 414.6 836.7 2313.1 4883.4 8428.7 10,234.4
Total personal income of the country (in billions of dollars) for selected years from 1956 to 2001 is given in the table.
(a) These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years after 1956.
(b) If this model is accurate, what will be the country's total personal income in 2006?
(c) In what year does the model predict the total personal income will reach $23 trillion?
(a) The equation of an exponential function that models the data is y=
(Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)
(b) The country's total personal income in 2006 will be $ billion.
(Round to three decimal places as needed.)
(c) The total personal income will reach $23 trillion in the year
(Round up to the nearest year.)
Transcribed Image Text:Total personal income of the country (in billions of dollars) for selected years from 1956 to 2001 is given in the table. (a) These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years after 1956. (b) If this model is accurate, what will be the country's total personal income in 2006? (c) In what year does the model predict the total personal income will reach $23 trillion? (a) The equation of an exponential function that models the data is y= (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) (b) The country's total personal income in 2006 will be $ billion. (Round to three decimal places as needed.) (c) The total personal income will reach $23 trillion in the year (Round up to the nearest year.)
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