Question

A person x inches tall has a pulse rate of y beats per minute, as given approximately by y=582x⁻¹/³

for 30≤x≤75 What is the instantaneous rate of change of pulse rate for the following heights? (A) 38 -inches (B) 61-inches What is the instantaneous rate of change of pulse rate for a 38 inch tall person? beats per minute per inch (Round to the nearest hundredth as needed.)

Answer 1

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.