Question 118258
The stabilization ratio (births/deaths) for south and central america can be modeled by the formula: y= -0.0012x2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x.
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{{{ graph( 300, 200, -20, 100, -2, 5, -.0012x^2+.074x+2.69) }}}
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a)Use the graph to estimate the year in which the stabilization ratio was at its maximum.
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Maximum looks to be around 30: 1950 + 30 = 1980
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b)Use the formula to find the year in which the stabilization ratio was at its maximum.
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Find the axis of symmetry: x = -b/(2a); a=-.0012; b=+.074
x = {{{-.074/(2*-.0012)}}} = 30.8333 ~ 31
1950 + 31 = 1981 year of max stabilization ratio
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c)what was the maximum stabilization ratio from part (b)?
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Substitute 30.83 for x, in the original equation; You should get y ~ 3.83
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d)what is the significance of a stabilization ratio of 1?
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I would imagine that means that deaths and births are equal
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