The equation y= -1777x + 27,153 can be used to predict the number y of gun deaths in the United States x years after 2000, that is x=0 corresponds to 2000, x=2 corresponds to 2002, x=5 corresponds to 2005, and so on. Predict the number of gun deaths in 2005 and 2009, In what year will the number of gun deaths be 9383?
The predicted number of gun deaths in 2005 will be?
The predicted gun deaths in 2009 will be?
The predicted number of gun deaths will be 9383 in the year?
For 2005, x = 5 so
y = -1777*5 + 27,153. Solve for y.
For 2009, x = 9 so
y = -1777*9 + 27,153. Solve for y.
For the number when y = 9383, set up
y = -1777*x + 27,153
substitute 9383 for y.
9383 = -1777*x + 27,153.
Solve for x. Then convert x to the year.
Check my thinking. Check my work.
To predict the number of gun deaths in a specific year based on the equation y = -1777x + 27,153, where x represents the number of years after 2000, you need to substitute the corresponding value of x into the equation and calculate y.
Let's calculate the predicted number of gun deaths in 2005 (x = 2005 - 2000 = 5):
y = -1777(5) + 27,153
y = -8,885 + 27,153
y ≈ 18,268
Therefore, the predicted number of gun deaths in 2005 is approximately 18,268.
Now let's calculate the predicted number of gun deaths in 2009 (x = 2009 - 2000 = 9):
y = -1777(9) + 27,153
y = -15,993 + 27,153
y ≈ 11,160
Therefore, the predicted number of gun deaths in 2009 is approximately 11,160.
To determine the year when the number of gun deaths will be 9383, we need to solve the equation for x:
9383 = -1777x + 27,153
First, let's isolate -1777x:
-1777x = 9383 - 27,153
-1777x = -17,770
Now divide both sides by -1777:
x ≈ -17,770 / -1777
x ≈ 10
Therefore, the number of gun deaths will be 9383 in the year 2010 (x = 10 + 2000).
To summarize:
- The predicted number of gun deaths in 2005 is approximately 18,268.
- The predicted number of gun deaths in 2009 is approximately 11,160.
- The number of gun deaths will be 9383 in the year 2010.