Question: The function that models the population (in thousands) of U.S. boys age 5 and under t years after 2010 is B(t) = -3.17t 2 +

The function that models the population (in thousands) of U.S. boys age 5 and under t years after 2010 is B(t) = -3.17t² + 119t + 10253and a function that models the population (in thousands) of U.S. girls age 5 and under t years after 2010 is G(t) = -3.02t² + 114t + 9802.

1) Find the equation that models the total estimated population (in thousands) of all U.S. children age 5 and under t years after 2010.

2) Use the equations given and the equation you found in part 2 to predict the number of boys, the number of girls and then the total number of children in the U.S. that are age 5 and under in a year of your choice (after 2010 but before 2021).

3) Go to the following websiteand determine the actual number of children in the U.S. that are age 5 and under in a year of your choice in part 2. (website data is added as a picture. below)

4) What does your answer in part 3 tell you about the validity of the model you found in part 1?

POP1 Child population: Number of children (in millions) ages 0-17 in the United States by age, 1950-2021 and projected 2022-2050 POP1 Excel Table 1966 1967 1968 1969 1958 1959 1961 1962 1963 1964 1965 1960 69.8 69.7 69.9 69.9 89.9 1952 1953 1954 1955 1956 1957 81.3 63.1 64.5 65.8 67.1 68.4 89.7 1950 1951 Number (in millions) 52.1 53.9 55.7 57.5 50.5 47.3 48.8 50.5 23.9 23.4 22.6 21.9 21.3 24.5 24.3 All children 24.3 24.7 24.7 24.1 24.5 24.8 24.8 21.5 22.0 22.6 23.2 23.7 22.3 22.8 23.4 23.8 24.2 24.4 Age 20.0 21.4 21.8 23.2 23.7 19.1 21.0 21.1 19.6 21.4 18.9 20.4 19.7 20.6 21.6 21.6 22.1 22.6 Ages 0-5 16.2 17.5 18.4 18.4 19.0 1989 15.3 15.8 16.3 17.6 1984 1985 1986 1987 1988 15.9 Ages 6-11 13.6 14.0 14.8 15.4 1983 13.1 1981 12.9 13.3 1980 1982 62 9 83.1 63.2 63.5 1975 1976 1977 1978 1979 1974 63.2 62.8 62.6 82 5 62.6 Ages 12-17 1970 1971 1972 1973 64.8 63.7 65 5 641 Number (in millions) 60.4 68.8 68.0 67.2 66.3 69.8 69.8 21.7 21.8 22.1 21.1 21.5 All children 19.6 20.0 20.5 20.8 21.4 20.4 20.9 21.3 18.9 18.9 19.2 19.3 19.5 19.4 19.6 20.0 Age 20.8 20.6 20.2 19.9 19.7 19.9 20.9 21.7 21.3 21.0 20.5 21.5 20.8 20.4 20.1 22.4 22.2 22.0 21.6 21.3 21.0 Ages 0-5 24.6 24.3 23.9 23.2 22.6 22.1 22.8 2009 25.4 25.3 25.0 24.6 23 9 23.3 2003 2004 2005 2006 2007 2008 Ages 6-11 24.7 25.0 25.3 25.5 1999 2000 2001 2002 1998 73.5 73.8 74.0 74.1 74.1 24.3 1997 73.3 Ages 12-17 1996 72.4 72.9 73.1 1990 1991 1992 1993 1994 1995 72.7 68.6 69.5 70.2 70.9 71.4 71.9 Number (in millions) 67.6 24.3 24.3 64.2 35.3 86.5 24.0 24.1 All children 23.4 23.6 23.8 23.3 24.3 23.1 23.1 23.2 23.8 23.9 24.1 23.5 23.7 23.7 23.5 23.3 23.2 24.9 24.8 24.3 24.0 23.8 Age 25.5 22.5 22.9 23.3 25.8 23.0 23.6 24.0 24.5 24.8 25.0 26.0 Ages 0-5 22.7 24.3 24.6 25.1 25.4 25.7 25.9 26.0 22.5 2029 22.2 2028 21.6 22.0 24.0 2027 Ages 6-11 21.8 22.2 22.7 23.1 23.5 23.8 2023 2024 2025 2026 20.1 20.4 21.0 2018 2019 2020 2021 2022 74.8 75.0 75.2 75.4 2014 2015 2016 2017 73.6 74.3 74.4 74.6 74.7 Ages 12-17 2012 2013 2010 2011 73.8 73 4 73.1 74.2 73.6 73.7 Number (in millions) 25.2 74.1 73.9 73.7 73.6 73.7 25.1 25.2 25.0 25.0 25.1 All children 22.9 24.8 24.9 24.0 24.7 24.9 25.2 23.8 23.8 23.4 25.0 25.3 23.9 Age 24.1 24.0 23.9 23.9 24.7 24.5 24.3 24.4 24.6 24.8 24.8 24.9 24.3 24.2 24.5 24.9 24.8 Ages 0-5 24.5 24.6 24.7 24.7 24.7 24.7 24.6 25.0 26.1 26.2 25.1 25.1 25.0 2045 2046 2047 2048 2049 24.6 24.6 25.0 Ages 6-11 25.1 25.0 25.0 25.0 25.0 25.1 2041 2042 2043 2044 25.1 2039 2040 77.6 77.7 77.8 77.9 78.1 25.3 2036 2037 2038 77.4 77.5 Ages 12-17 2035 2031 2032 2033 2034 76.9 77.0 77.1 77.1 77.2 77.3 2030 76.8 Number (in millions) 75.9 76.1 76.3 76.5 76.7 25.7 25.7 25.8 25.9 75.7 25.5 25.6 All children 25.5 26.0 25.3 25.3 25.4 25.4 25.8 25.9 25.9 Age 25.2 25.2 25.2 25.3 25.3 25.7 25.7 25.7 25.8 25.2 25.2 25.2 25.7 25.7 25.2 25.7 25.7 25.7 26.2 26.2 26.2 26.2 26.2 26.2 26.2 Ages 0-5 25.6 25.6 25.6 25.6 28.1 26.1 26.2 25.4 25.5 25.5 28.1 Ages 6-11 25.5 25.7 25.8 25.9 26.0 26.0 25.1 25.2 25.4 Ages 12-17 2050 Number (in millions) 78.2 All children Age 25.9 Ages 0-5 26.0 Ages 6-11 26.3 Ages 12-17

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