The rate of increase of the number of married couples M (in thousands) in a coun

Question

The rate of increase of the number of married couples M (in thousands) in a country from 1970 to 2005 can be modeled by the equation below where t is the time in years, with t = 0 corresponding to 1970. The number of married couples in 2005 was 60,040 thousand. dM dt = 1.218t2 ? 44.72t + 709.1 (a) Find the model for the number of married couples in the country. M(t) = (b) Use the model to predict the number of married couples in the country in 2017. Does your answer seem reasonable? Explain your reasoning.

Explanation / Answer

dM/dt=1.218t2 44.72t + 709.1

M(t)=(1.218/3)t3-(44.72/2)t2+(709.1)t+c

M(1970=0)=C

M(35)=60040=0.406.(35)3 -22.36(35)2 +709.1(35)+C

C=60040-14834.75=45205.25~45205

M(12+35)=M(47)=0.406.(47)3 -22.36(47)2 +709.1(47)+45205=71291.598~71291

yes as it is a increasing function

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