The bar graph shows the cumulative number of death form AIDS in the US, from 1990 through each of the years 1996-2002.
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) = -2209xto the 2 power + 57.571x +107898
G(x) = -82 x to the 3 power +50613x +113438
Find f(x) and g(x)
I have try to work the problem out, however I am not able to figure it out.
To find the values of f(x) and g(x) for given x years after 1990, we can substitute the values of x into the corresponding polynomials.
For f(x):
f(x) = -2209x² + 57.571x + 107898
For g(x):
g(x) = -82x³ + 50613x + 113438
To find f(x) and g(x) for specific years, substitute the value of x into the respective equations. For example, if you want to find the values for x = 1996, substitute x = 6 into the equations:
For f(x):
f(6) = -2209(6)² + 57.571(6) + 107898
For g(x):
g(6) = -82(6)³ + 50613(6) + 113438
Simplifying each equation will give you the values of f(x) and g(x) for the given years after 1990.
To find the values of f(x) and g(x) at a particular year, you simply substitute the year value into the respective polynomial equations.
For f(x), the polynomial is:
F(x) = -2209x^2 + 57.571x + 107898
To find f(x) at a specific year, let's say 1996, you substitute x = 6 (1996 - 1990) into the equation:
F(6) = -2209(6)^2 + 57.571(6) + 107898
Simplifying the equation, we have:
F(6) = -2209(36) + 345.426 + 107898
F(6) = -79644 + 45208.426 + 107898
F(6) = 74163.426
So, f(6) = 74163.426
Similarly, for g(x), the polynomial is:
G(x) = -82x^3 + 50613x + 113438
To find g(x) at a specific year, let's say 2002, you substitute x = 12 (2002 - 1990) into the equation:
G(12) = -82(12)^3 + 50613(12) + 113438
Simplifying the equation, we have:
G(12) = -82(1728) + 607356 + 113438
G(12) = -141696 + 607356 + 113438
G(12) = 579098
So, g(12) = 579098
Therefore, f(x) = 74163.426 and g(x) = 579098.