algebra

[pslagle]

Stabilization ratio. The stabilization ratio (births/deaths) for South and Central America can be modeled by the formula:
y=-0.0012x^2+0.074+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 stabiliation ratio was at its maximum - although you cannot see the graph it shows 1980 as the year. (1950 +30=1980).
b)Use the formula to find the year in which the stabilization ratio was at its maximum.
y=-0.0012(30)^2+0.074(30)+2.69
y=-0.0012(900)+2.22+2.69
y=-1.08+2.22+2.69
y=3.83
c) what is the significance of a stabilization ratio of 1?

 

[Gene]

Once again your typing needs looking at before you click on submit! It is nicer to have the equation correct.
y=-0.0012x^2+0.074x+2.69
Part a) is probably as good as you can read from a graph.
Part b) says to use the formula. I suspect it means -b/2a which is the x coordinate of the vertex of the parabola and is slightly different from 30.

 

[pslagle]

you are absolutely right with my typing. I must apologize because I do not understand your answer to b.

 

[Gene]

There are several ways of finding the vertex of a parabola from the equation ax²+bx+c. The simplest is that x= -b/2a which is the one I used. Another is to use the quadratic formula
x=(-b+sqrt(b²-4ac))/2a
and the vertex is half way between those two x values. Since they are asking for it, they must have given you some method. Any one would do, but they don't want it taken from the graph.