Final answer:
The instantaneous rate of change of pulse rate for a person who is 38 inches tall is approximately -5.37 beats per minute per inch, showing a decrease in the pulse rate with each additional inch of height.
Step-by-step explanation:
The student is asking about the instantaneous rate of change of a pulse rate function given for a person's height. The pulse rate (y) as a function of height (x) is given by y = 582x-1/3. The instantaneous rate of change is found by taking the derivative of the pulse rate function with respect to height.
For a person who is 38 inches tall, the instantaneous rate of change is found by evaluating the derivative at x = 38. Let's first find the derivative dy/dx:
dy/dx = d(582x-1/3)/dx
dy/dx = 582 * (-1/3) * x-4/3
Now, we substitute x = 38 into the derivative:
dy/dx |x=38 = 582 * (-1/3) * (38)-4/3
dy/dx |x=38 ≈ -5.370 beats per minute per inch (rounded to the nearest hundredth).
The instantaneous rate of change for a person 38 inches tall is approximately -5.37 beats per minute per inch, indicating that for each additional inch of height, the pulse rate decreases by about 5.37 beats per minute.