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In 2010, about 159,000 American high school students participated in
lacrosse, and in 2012, about 176,000 participated.
a. Create a graph to show the number of participants in lacrosse based on the change
in participation from 2010 to 2012.
b. Based on the data, what is the annual growth of the sport?
c. If participation continues at the same rate, what will be the participation in 2020 to
the nearest 1000?

Answer :

Using a linear function, it is found that:

a) The graph is given at the end of this answer. The x-axis is the number of years after 2010, while the y-axis is the number of participants, in thousands.

b) 8,500 more participants per year.

c) The estimate is of 244,000 participants in 2020.

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The equation of a linear function has the following format:

[tex]y = mx + b[/tex]

In which

  • m is the slope, that is, the rate of change.
  • b is the y-intercept, that is, the initial value.

  • Initially, in 2010, there was 159,000 participants, thus [tex]b = 159[/tex].
  • In 2012, which is 2012 - 2010 = 2 years after, 176,000 participants, thus, the slope is:

[tex]m = \frac{176 - 159}{2} = 8.5[/tex]

Then, the function is:

[tex]y = 8.5x + 159[/tex]

The graph is given at the end of this answer. The x-axis is the number of years after 2010, while the y-axis is the number of participants, in thousands.

Item b:

  • The rate of change is the slope, which is of 8,500 more participants per year.

Item c:

  • 2020 is 2020 - 2010 = 10 years after 2010, thus this is y(10).

[tex]y = 8.5x + 159 = 8.5(10) + 159 = 244[/tex]

The estimate is of 244,000 participants in 2020.

A similar problem is given at https://brainly.com/question/20849340

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