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 Source: Based on data from Statistical Abstract 2001. a. Find the number of homicides of 15 - to 19-year-olds in the United States in 1992. (1992 is 2 years after 1990, so t = 2 ) b. Find the number of homicides of 15- to 19-year-olds in the United States in 2002. c. In what year was the number of homicides 7337?

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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