SOLUTION: Word problem-The number of case of HIV/AIDS worldwide is modeled by the equation y=2x+33, where y represents the number of HIV/AIDS cases, in millions, and x reprsents the number o
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Question 69669: Word problem-The number of case of HIV/AIDS worldwide is modeled by the equation y=2x+33, where y represents the number of HIV/AIDS cases, in millions, and x reprsents the number of years since 1999 (i.e., the beginning of 1999 corresponds to x=0).
a) Going by the equation, how many people with HIV/AIDS were there in 2002?
b) If it continues, in what year will the number of cases reach 60 million?
c) How much do the number of people with HIV/AIDS increase or decrease each year?
d) Graph the equation, for the years between 1999 and 2019?
Found 2 solutions by stanbon, tutorcecilia:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y=2x+33, where y represents the number of HIV/AIDS cases, in millions, and x reprsents the number of years since 1999 (i.e., the beginning of 1999 corresponds to x=0).
a) Going by the equation, how many people with HIV/AIDS were there in 2002?
y=2(2002-1999)+33= 2*3+3 = 9 million
-------------------
b) If it continues, in what year will the number of cases reach 60 million?
60=2x+33
2x=27
x=13.5
1999+13.5 = 2012.5
It will happen in 2012
------------------
c) How much do the number of people with HIV/AIDS increase or decrease each year?
The slope of the equation is 2 meaning an increase of 2 million each year
-----------------
d) Graph the equation, for the years between 1999 and 2019?
---------------
Cheers,
Stan H.
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
y=2x+33 [plug-in the values for x and solve for y]
y=2(0)+33 [x=0 in 1999; solve for y]
y=33Million
Create a table of values:
x........................y
1999(0)......33M
2000(1)......35M
2001(2)......37M
2002(3)......39
2003(4).......41
2004(5).......43
2005(6).......45
2006(7).......47
etc.
.
a) Going by the equation, how many people with HIV/AIDS were there in 2002?
y=2x+33 [plug-in x=3 (2002) and solve for y]
y-2(3)+33
y=6+33
y=39Million cases
.
b) If it continues, in what year will the number of cases reach 60 million?
y=2x+33 [Let y=60M and solve for x]
60=2x+33
60-33=2x
27=2x
27/2=2x/2
13.5=x or year 2012.5
.c) How much do the number of people with HIV/AIDS increase or decrease each year?
Use the slope to solve.
m=2 or m=2/1
So for every one year, 2 million cases are added.
.
d) Graph the equation, for the years between 1999 and 2019?
For 2019, let x=20
y=2(20)+33
y=40+33
y=73
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