Cumulative Number of Deaths from AIDS 483,920
500,000
458,551
450,000
The bar graph shows the cumulative number of
deaths from AIDS in the United States, from 1990
through each of the years 1996 to 2002
The data in the graph can be modeled by the
following polynomials, in which f(x) and g(x)
represent the cumulative number of AIDS deaths x
years after 1990
f(x) = - 2217x2.57,570x + 107.896
g(x) = -86x3 - 698x2 + 50, 612x + 113.438
Number of Deaths
400,000
350.000
8
Year
Use f(x) to find the cumulative number of AIDS deaths in 2002
(Simplify your answer)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be