Heart Rate An athlete starts running and continues
for 10 seconds. The polynomial calculates
the heart rate of the athlete in beats per minute
t seconds after beginning the run, where .
(a) What is the athlete’s heart rate when the athlete
first starts to run?
(b) What is the athlete’s heart rate after 10 seconds?
(c) What happens to the athlete’s heart rate while the athlete is running?
What is the polynomial?
c. It increases.
To answer these questions, we need to understand the given information and use it to analyze the polynomial that calculates the athlete's heart rate. Here are the steps to find the answers:
Step 1: Understand the polynomial equation
The polynomial equation calculates the heart rate of the athlete in beats per minute at time t seconds after beginning the run. Let's assume the polynomial equation is given by HR(t).
Step 2: Identify the specific values
(a) To find the athlete's heart rate when they first start running, we need to find HR(0) because the athlete hasn't started running yet. HR(0) will give us the heart rate immediately at the beginning of the run.
(b) To find the athlete's heart rate after 10 seconds, we need to find HR(10) because it represents the heart rate 10 seconds after starting the run.
(c) To understand what happens to the athlete's heart rate while running, we need to analyze the trend or behavior of the polynomial equation. We can observe this by simplifying the equation, graphing it, or analyzing its properties.
Step 3: Calculate the answers
(a) Calculate HR(0) by substituting 0 into the polynomial equation and solving for HR(0). The resulting value will be the heart rate when the athlete first starts running.
(b) Calculate HR(10) by substituting 10 into the polynomial equation and solving for HR(10). The resulting value will be the heart rate after 10 seconds of running.
(c) Analyze the behavior of the polynomial equation by simplifying it, graphing it, or analyzing its properties. This will help determine what happens to the athlete's heart rate while running. It could be an increasing, decreasing, or constant heart rate based on the properties of the polynomial.
By following these steps, you should be able to find the answers to the given questions about the athlete's heart rate while running.