Question 61024
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 
{{{ graph( 300, 200, -10, 80, -1, 5, -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 = {{{(-.074)/(2*-.0012)}}} = {{{(-.074)/(-.0024)}}} = 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?