I am having problems figuring out some of my word problems for this week. Could someone check these?
The equation y=-1777x+27,153 can be used to predict the number of gun deaths in the U. S. x years after 2000, that is, x=0 corresponds to 2000, x=2, corresponds with 2002, x=5, corresponds with 2005 and so on. Predict the number of gun deaths in 2005 and 2007. In what year will the number of gun deaths be 12,937?
2005-18,268
2007-14,714
it will be 12,937 in 2008
yes.
-1777*5 +27153 = 18 268
-1777*7 +27153 = 14 714
12 937 = -1777 x + 27153
x = 8 so 2008 check
To solve this problem, we need to substitute the given values of x into the equation y = -1777x + 27,153.
To find the number of gun deaths in 2005, we substitute x = 5 into the equation:
y = -1777(5) + 27,153
y = -8,885 + 27,153
y = 18,268
So, the predicted number of gun deaths in 2005 is 18,268.
To find the number of gun deaths in 2007, we substitute x = 7 into the equation:
y = -1777(7) + 27,153
y = -12,439 + 27,153
y = 14,714
So, the predicted number of gun deaths in 2007 is 14,714.
To find the year when the number of gun deaths is 12,937, we need to solve the equation for y = 12,937:
12,937 = -1777x + 27,153
Rearranging the equation to isolate x:
-14,216 = -1777x
Dividing both sides by -1777:
x = -14,216 / -1777
x ≈ 7.98
Since x corresponds to the number of years after 2000, we round up to 8. Therefore, in the year 2008, the predicted number of gun deaths will be 12,937.
So, your answers are:
Number of gun deaths in 2005: 18,268
Number of gun deaths in 2007: 14,714
Year with 12,937 gun deaths: 2008