The number of children (in thousands) receiving Social Security benefits for each year from 1988 to 1995 can be modeled using the polynomial N(t)=-3.7475t3+ 50.9437t2 - 97.3413t + 3207.6818 where t is time in years since 1988. a.) Graph this function on the domain [0,20]. b.) What is the value of the y-intercept, and what does this tell you in practical terms? c.) How many children on Social Security does this model predict for the year 1990? (3,186,000 children is the actual number for that year). d.) Is there a point at which this model stops being useful? In other words, what is a reasonable, practical domain for this function? (There are many possible answers.) Explain your answer.
1.) The number of children (in thousands) receiving Social Security benefits for each year from 1988 to 1995 can be modeled using the polynomial N(t)=-3.7475t3+ 50.9437t2 - 97.3413t + 3207.6818 where t is time in years since 1988.
a.) Graph this function on the domain [0,20].
b.) What is the value of the y-intercept, and what does this tell you in practical terms?
c.) How many children on Social Security does this model predict for the year 1990? (3,186,000 children is the actual number for that year).
d.) Is there a point at which this model stops being useful? In other words, what is a reasonable, practical domain for this function? (There are many possible answers.) Explain your answer.
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