Question

Cumulative Number of Deaths from AIDS 483,920 458,551 500,000 450,000 400,000 350,000 Year

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. (SHOW WORK)

f(x) = -2209x² + 57,573x + 107,896

g(x) = -83x³ - 698x² + 50,614x + 113,432

a) Use? f(x) to find the cumulative number of AIDS deaths in 2000.

b) Use? g(x) to find the cumulative number of AIDS deaths in 2000.

c) Which function is a better description for the actual number shown in the bar? graph?

f(x) or g(x) or Cannot be determined

Answer 1

Here, given a bar graph shows the cumulative number of deaths from AIDS in the United​ States, from 1990 through each of the years 1996 to 2002

This data can be modelled by the polynomials f(x),g(x).

f(x) = -2209x2 + 57,573x + 107,896

g(x) = -83x3 - 698x2 + 50,614x + 113,432

a) Finding the cumulative number of AIDS deaths in 2000 using f(x).

f(x) = -2209x2 + 57,573x + 107,896

Here,x=10 years because x in the polynomial is years after 1990.

2000 is 10 years after the 1990.

Substitute, x=10 years in f(x)

f(x) = -2209x2 + 57,573x + 107,896

f(10)= -2209 (10)²+ 57,573(10) + 107,896

= -2209(100) + 57,573(10) + 107,896

= -220900+575730+107896

= 462726

Therefore, the cumulative number of AIDS deaths in 2000 is 462,726

b) Finding the cumulative number of AIDS deaths in 2000 by using g(x):

g(x) = -83x3 - 698x2 + 50,614x + 113,432

Here,x=10 years because x in the polynomial is years after 1990.

2000 is 10 years after the 1990.

Substitute, x=10 years in g(x)

g(x) = -83x3 - 698x2 + 50,614x + 113,432

g(10)= -83(10)³ - 698(10)² + 50,614(10) + 113,432

= -83000-69800+506140+113432

= 466,772

Therefore, the cumulative number of AIDS deaths in 2000 is 466,772.

c) f(10)= 462,726 and g(10)= 466,772

From the graph, the cumulative number of AIDS deaths in 2000 is 458,551

By observing the f(10), g(10) and cumulative number of AIDS deaths in 2000, it is clear that f(10) is a near value to the actual value.

So, the function f(x) is a better description for the actual number shown in the bar​ graph.