c Think of whether the number of seats in the stadium is infinite.
D
d Is the slope negative or positive? What does it tell us about the change of attendance?
A
a1657
B
b468962
C
c No; the number of seats in the stadium is limited.
D
d Yes, see solution.
Practice makes perfect
a We know that in 2001 the attendance during Indianapolis Colts matches was 45074,6 and the attendance in 2005 was 457373. Let the x-axis represent the number of years after the year 2000 and the y-axis represent the number of people who attended the matches. We can then form the ordered pairs written below.
(1,450746)and(5,457373)
If we substitute these points into the Slope Formula we can calculate the slope.
The approximate rate of change in attendance from 2001 to 2005 was 1657 people per year.
b In order to predict the attendance for 2012, we need to find the equation that describes this situation. From the previous part we know that the slope is 1657. Let's substitute it and the point (1,450746) into the point-slope form.
y−y1=m(x−x1)⇓y−450746=1657(x−1)
Now, since we want to calculate the attendance in 2012, we can substitute x with 12 and solve the equation for y.
c The attendance will not continue to increase indefinitely, because the number of seats in a stadium are limited. Someday the last seat will be taken and no additional people will be able to attend the game.
d The decision to build a new, larger stadium was reasonable, because the slope that we found earlier is positive. This means that more and more people attend the matches each year, so someday there could be no place for everyone who came to watch the game. Therefore, if the trend continues, the decision to build the bigger stadium will pay off.
Mathleaks uses cookies for an enhanced user experience. By using our website, you agree to the usage of cookies as described in our policy for cookies.
