SOLUTION: The number of workers per social security beneficiary has been declining approximately linearly since 1970. In 1970, there were 3.7 workers per beneficiary. In 2050 it is projected

Question 1103314: The number of workers per social security beneficiary has been declining approximately linearly since 1970. In 1970, there were 3.7 workers per beneficiary. In 2050 it is projected there will be 2.0 workers per beneficiary. Let W be the workers per social security beneficiary and t be the number of years since 1970.
a) Find the function W (t) that fits the data.
b) Estimate the number of workers per beneficiary in 2020.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The number of workers per social security beneficiary has been declining approximately linearly since 1970. In 1970, there were 3.7 workers per beneficiary. In 2050 it is projected there will be 2.0 workers per beneficiary. Let W be the workers per social security beneficiary and t be the number of years since 1970.
a) Find the function W (t) that fits the data.
Let 1970 be zero, then 2050 = 80
Equation Form:: W(t) = m*t + b
(0,3.7); (80,2)
slope = (2-3.7)/(80-0) = -1.7/80 = -0.02125
b is W(0) = 3.7
Equation::
W(t) = -0.02125*t + 3.7
b) Estimate the number of workers per beneficiary in 2020.
Note:: If 1970 is zero, 2020 is 50
Ans: W(50) = -0.2125*50 + 3.7 = 2.6375 workers
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Cheers,
Stan H.
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