12. According to a study conducted by Rutgers University, the median age of wome

Question

12. According to a study conducted by Rutgers University, the median age of women in the U.S. at first marriage is approximated by the function f(t) -0.083 t+0.6 t+0.18t +20.1 (0srs5) where t is measured in decades and 0 corresponds to the beginning of 1960. a) What was the median age of women at first marriage at the beginning of 19602 (2 pts) The medi an ae oS b) What was the median age of women at first marriage at the beginning of 2000? (2pts)the median gee of womeetn 200 The m edi an aee ag wome 2o c) When was the median age of women at first marriage changing most rapidly ove time period under consideration? (4 pts) was o

Explanation / Answer

f = -0.083t^3 + 0.6t^2 + 0.18t + 20.1

Beginning og 1960, so t = 0...

Plug in, we get :
f(0) = 20.1

So, median age = 20.1 yrs

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b)
Beginning of 2000,
so plug in t = 4 cuz we dealin' with decades here...
2000 is the 4th decade since 1960...

So, t = 4

f = -0.083t^3 + 0.6t^2 + 0.18t + 20.1

f = -0.083(4)^3 + 0.6(4)^2 + 0.18(4) + 20.1

25.108 yrs

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c)
Changing most rapidly...

df/dt = -0.249t^2 + 1.2t + 0.18 = 0

Solving, we get :
t = -0.145601 and t = 4.96488

So, clearly t = 5 approx

So, the median age was changing most rapidly
during the beginning of 2010

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