SOLUTION: 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 num

Algebra ->  Linear-equations -> SOLUTION: 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 num      Log On


   

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.
a)Use the graph to estimate the year in which the stabilization ratio was at its maximum.
b)Use the formula to find the year in which the stabilization ratio was at its maximum.
c)what was the maximum stabilization ratio from bart (b)?
d)what is the significance of a stabilization ratio of 1?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
:
+graph%28+300%2C+200%2C+-20%2C+100%2C+-2%2C+5%2C+-.0012x%5E2%2B.074x%2B2.69%29+
:
a)Use the graph to estimate the year in which the stabilization ratio was at its maximum.
:
Maximum looks to be around 30: 1950 + 30 = 1980
:
:
b)Use the formula to find the year in which the stabilization ratio was at its maximum.
:
Find the axis of symmetry: x = -b/(2a); a=-.0012; b=+.074
x = -.074%2F%282%2A-.0012%29 = 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)?
:
Substitute 30.83 for x, in the original equation; You should get y ~ 3.83
:
:
d)what is the significance of a stabilization ratio of 1?
:
I would imagine that means that deaths and births are equal
:
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