Question

PLEASE HELP!! I need all the work shown please!!

APH hows the heart rate of a runner during a 4 minute interval.

Please describe the following:
1. The range of the runner's heart rate
2. The intervals where the runner's heart rate is increase
3. The interval where the runner's heart rate is decreasing.
4. The interval where the runner's heart rate is staying the same.
5. Create an equation to represent the linear portions between 2 and 3 minutes AND the range between 3 and 4 minutes.
6. Explain what you think is happening to cause these changes in heart rate.

Please explain all steps and show all work!

Answer 1

1- The range of the runner's heart rate is 60 to 110.

2- The interval where the runner's heart rate is increasing is from second 0 to second 2.

3- The interval where the runner's heart rate is decreasing is not mentioned in the given information.

4- The interval where the runner's heart rate is staying the same is from second 2 to second 4.

5- To create an equation to represent the linear portions between 2 and 3 minutes, we need to first determine the slope of the line. The slope is the change in heart rate (y-value) divided by the change in time (x-value). In this case, the change in heart rate is 80 - 60 = 20 and the change in time is 2 - 0 = 2. Therefore, the slope of the line is 20/2 = 10.

To find the equation of the line, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1). In this case, y1 is the starting heart rate of 60 at time x1 = 0. Substituting these values into the equation, we get: y - 60 = 10(x - 0). Simplifying this equation, we get: y = 10x + 60.

To find the equation of the range between 3 and 4 minutes, we can use the same method. The starting heart rate at time x1 = 3 is 80 and the ending heart rate at time x2 = 4 is above 110. The change in heart rate is 110 - 80 = 30 and the change in time is 4 - 3 = 1. Therefore, the slope of the line is 30/1 = 30. Using the point-slope form of a linear equation, we get: y - 80 = 30(x - 3). Simplifying this equation, we get: y = 30x + 50.

6- It is difficult to determine what is causing the changes in heart rate without more information. Heart rate can be affected by many factors, including physical activity level, age, fitness level, and underlying medical conditions. It is possible that the runner's heart rate increased at the beginning of the interval due to the increased physical activity, and remained constant for the next two minutes because the activity level was sustained. The sudden increase in heart rate at the end of the interval could be due to a variety of factors, such as a burst of energy or a reaction to some external stimulus.