The equation y = 1777x + 27,153 can be used to predict the number y of gun deaths in the U.S.x years after 2000, that is x = 0 corresponds to 200, x2 corresponds to 2002,x5 crresponda with 2005, and so on. Predice the number of gun deaths in 2005 ad 2007. In what year will the number od deaths be 11,160?
So your equation is really
y = 1777 (year -2000) + 27153
so for 2007 for example
y = 1777 (2007-2000) + 27153
y = 12439 + 27153
= 39,592 in 2007
do other years the same way
for the second part unless you have a typo we are talking about before 2000
11,160 = 1777(year -2000 ) + 27153
1777(year-2000) = - 15993
year - 2000 = -9
year = 1991
To find the number of gun deaths in 2005 and 2007, we need to substitute the corresponding values of x into the equation.
Let's start with 2005 (x = 2005 - 2000 = 5):
y = 1777x + 27,153
y = 1777 * 5 + 27,153
y = 8,885 + 27,153
y = 36,038
Therefore, the predicted number of gun deaths in 2005 is 36,038.
Now, let's find the number of gun deaths in 2007 (x = 2007 - 2000 = 7):
y = 1777x + 27,153
y = 1777 * 7 + 27,153
y = 12,439 + 27,153
y = 39,592
Hence, the predicted number of gun deaths in 2007 is 39,592.
Next, let's find the year when the number of deaths will be 11,160.
11,160 = 1777x + 27,153
Now, let's solve for x:
Subtract 27,153 from both sides:
11,160 - 27,153 = 1777x
Combine like terms:
-15,993 = 1777x
Divide both sides by 1777:
x = -15,993 / 1777
x ≈ -9
Since x represents years after 2000, we can conclude that the number of deaths would be 11,160 approximately 9 years before 2000, which would be around the year 1991.
So, in 1991, the number of gun deaths would be predicted to be 11,160.