Respuesta :
a. The number of homicides in the United States in 1992, using the given equation N = - 315.9t + 4809.8, is 4178.
b. The number of homicides in the United States in 1992, using the given equation N = - 315.9t + 4809.8, is 1019.
c. Using the equation N = - 315.9t + 4809.8, we can say that the year in which the number of homicides were 7337 was 1982.
In the question, we are given that the number of homicides, N, of 15- to 19-year-olds in the United States t years after 1990 can be represented by the equation N = - 315.9t + 4809.8.
We are asked:
a. to find the number of homicides of 15 - to 19-year-olds in the United States in 1992.
We know that 1992 is 2 years after 1990, making t = 2.
To find the number of homicides in the year 1992, we simply put t = 2 in the equation N = - 315.9t + 4809.8, to get:
N = - 315.9(2) + 4809.8,
or, N = - 631.8 + 4809.8,
or, N = 4178.
Thus, the number of homicides in the United States in 1992, using the given equation N = - 315.9t + 4809.8, is 4178.
b. to find the number of homicides of 15 - to 19-year-olds in the United States in 2002.
We know that 2002 is 12 years after 1990, making t = 12.
To find the number of homicides in the year 2002, we simply put t = 12 in the equation N = - 315.9t + 4809.8, to get:
N = - 315.9 (12) + 4809.8,
or, N = -3790.8 + 4809.8,
or, N = 1019.
Thus, the number of homicides in the United States in 1992, using the given equation N = - 315.9t + 4809.8, is 1019.
c. to find the year in which the number of homicides were 7337.
We are now given the number of homicides, that is, N = 7337.
To find the year, we simply put N = 7337 in the equation N = - 315.9t + 4809.8, to get:
7337 = - 315.9t + 4809.8,
or, 7337 - 4809.8 = - 315.9t,
or, 2527.2 = - 315.9t,
or, t = - 2527.2/315.9,
or, t = -8.
The year = 1990 + t = 1990 + (-8) = 1982.
Thus, using the equation N = - 315.9t + 4809.8, we can say that the year in which the number of homicides were 7337 was 1982.
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