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Problem 28 Medium Difficulty

The table shows how the average age of first marriage of Japanese women has varied since 1950.
(a) Use a graphing calculator or computer to model these data with a fourth-degree polynomial.
(b) Use part (a) to find a model for $ A'(t). $
(c) Estimate the rate of change of marriage age of women in 1990.
(d) Graph the data points and the models for $ A $ and $ A'. $

Answer

a) $A(t)=-0.000003 t^{4}+0.000362 t^{3}-0.013289 t^{2}+0.221834 t+23.018878$
b) $A^{\prime}(t)=-0.000012 t^{3}+0.001086 t^{2}-0.026578 t+0.221834$
c) about 0.11
d) Graph Unavailable

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Video Transcript

It's clear sailing rain here. So we're going to use a calculator to find and then we get a team is equal to naked in 00000 three t to the fourth plus 0.0 362 T x cube. You learn a syrah 0.1 3 to 8. Nine T square with 0.2 to 1 83 40. I was 23 come 01 e eight 70 for party. We're gonna find the derivative. You've been palatable, Josie. Quilting negative zero point Cyril Thereau throws Earl 12 He cute plus sirrah 0.1 Is there a girl? One through 8 60 square Munna zero point through, too. 6578 T plus 0.2 to 1 834 for it. See, we found a thief function and its derivatives. Were you gonna use the derivative function 40 when we get around 0.11 So the rate of change of first marriage increased by 0.11 in 1990 right, You're just gonna do a graph. So the x and Y access 2025. These are in intervals of five. In the graph we plot, it walks into this and then the derivative crap. Something like this