Question

trail running is one of the few sports that has been consistently increasing over the past few years. the number of people participating in trail running (in millions) from the years 2013 to 2018 is given by the equation y = 0.3x + 4, where x is the number of years after 2010.
a. use this equation or a graph of it to complete the ordered pair (7, ).
b. write a sentence explaining the meaning of the answer to part (a).
c. if this trend continues, how many trail runners will there be in 2033?
a. complete the ordered pair.

Explanation:

Step1: Substitute \(x = 7\) into the equation \(y=0.3x + 4\)

$$y=0.3\times7 + 4$$

Step2: Calculate the value of \(y\)

First, calculate \(0.3\times7=2.1\). Then, \(y = 2.1+4=6.1\)

Step3: Find \(x\) for the year 2033

Since \(x\) is the number of years after 2010, for 2033, \(x=2033 - 2010=23\)

Step4: Substitute \(x = 23\) into the equation \(y = 0.3x+4\)

$$y=0.3\times23+4$$

Step5: Calculate the value of \(y\)

First, calculate \(0.3\times23 = 6.9\). Then, \(y=6.9 + 4=10.9\)

Answer:

a. The ordered pair is \((7,6.1)\)
b. When \(x = 7\) (7 years after 2010), substituting into \(y = 0.3x+4\) gives \(y = 6.1\). This means that 6.1 million people participated in trail running 7 years after 2010.
c. There will be 10.9 million trail - runners in 2033.