SOLUTION: HELP! Stabilization ratio. The stabilization ratio (births / deaths) for south and central America can be model by the formula y = -0.0012x^2 + 0.074x + 2.69 where y is the number

Question 61024: HELP! Stabilization ratio. The stabilization ratio (births / deaths) for south and central America can be model by the formula y = -0.0012x^2 + 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 was at its maximum.
b. Use the formula to find the year in which the stabilization ratio was at its maximum.
c. What is the maximum stabilization ratio from part (b)?
d. What is the significance of a stabilization ratio of 1?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Stabilization ratio. The stabilization ratio (births / deaths) for south and central America can be model by the formula y = -0.0012x^2 + 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 was at its maximum.
Plot a graph of the given equation: y = -0.0012x^2 + 0.074x + 2.69

It looks like max is about x = 30 years, which is: 1950 + 30 = 1980
:
:
b. Use the formula to find the year in which the stabilization ratio was at its maximum.
Use the vertex formula: x = -b/(2a), a=-.0012, b=.074
:
x = = = 30.83 yrs (1980.83)
;
:
c. What is the maximum stabilization ratio from part (b)?
Substitute 30.83 for x in the original equation and find y:
You should get about 3.8
:
:
d. What is the significance of a stabilization ratio of 1?
That would mean the same number that die, are born, 0 population growth?

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