In Canada, the number of girls playing organized ice hockey from January 1990 to January 2010 increased by approximately 4162 girls per year. In January 2000, there were approximately 45 400 girls playing organized ice hockey.
a. Write an equation in slope-point form to represent the number of girls, n, playing organized ice hockey as a function of the number of years, t, after 1990.
b. Use the equation in part a) to estimate the number of girls playing organized ice hockey in January 2009.
slope = 4162
but when t = 10, n = 45400
so
n - 45400 = 4162 (t-10)
-----------------------------
n at t = 19
n = 45400 + 4162(9)
a. To write an equation in slope-point form, we need to find the slope and a point on the line. Given that the number of girls playing organized ice hockey increased by approximately 4162 girls per year, the slope of the line is 4162.
Using this information, we can write the equation as:
n = mt + b
where n represents the number of girls playing organized ice hockey, t represents the number of years after 1990, m represents the slope, and b represents the y-intercept.
Since the number of girls playing organized ice hockey in January 2000 was approximately 45,400, we can use this information to find the y-intercept.
Substituting the values into the equation:
45,400 = 4162(10) + b
Simplifying the equation:
45,400 = 41,620 + b
By rearranging the equation to solve for b, we get:
b = 45,400 - 41,620
Simplifying:
b = 3780
Therefore, the equation representing the number of girls, n, playing organized ice hockey as a function of the number of years, t, after 1990 is:
n = 4162t + 3780
b. To estimate the number of girls playing organized ice hockey in January 2009, we need to find the value of t for January 2009. Since January 1990 is the starting point, it would be 19 years after 1990.
Substituting t = 19 into the equation:
n = 4162(19) + 3780
Simplifying:
n = 79,178 + 3780
n ≈ 82,958
Therefore, the estimated number of girls playing organized ice hockey in January 2009 is approximately 82,958.
To find the equation in slope-point form, we need to determine the slope (rate of change) and a point on the line.
Given:
Number of girls playing organized ice hockey in January 2000 = 45,400.
From January 1990 to January 2010, the number of girls increased by approximately 4162 per year.
a. To find the slope, we need to calculate the change in the number of girls over the change in years. Let's represent the slope as m.
m = change in y / change in x
Change in y:
The number of girls increased by 4162 per year, which means for every year (change in x), there is an increase in 4162 girls (change in y).
Change in x:
We measure the change in years from 1990 to a specific year, t. So, the change in x is given by t - 1990.
Thus, the slope (m) = change in y / change in x = 4162 girls / (t - 1990) years.
Now, we need to find a point on the line. We know that in January 2000 (10 years after 1990), the number of girls playing organized ice hockey was 45,400.
So, the point on the line is (10, 45,400) (t = 10 years, n = 45,400 girls).
Therefore, the equation in slope-point form is: n - 45,400 = 4162(t - 10).
b. To estimate the number of girls playing organized ice hockey in January 2009, we substitute t = 19 (since January 2009 is 19 years after 1990) into the equation from part a).
n - 45,400 = 4162(19 - 10)
n - 45,400 = 4162 * 9
n - 45,400 = 37,458
n = 45,400 + 37,458
n ≈ 82,858
Hence, the estimated number of girls playing organized ice hockey in January 2009 is approximately 82,858.