In a healthy person of height inches, the average pulse rate in beats per minute is modeled by the formula 596/(x^.5) for 30<x<100. Using linear approximation, the estimate for the change in pulse that corresponds to a height change from 59 inches to 60 inches is
beatspermin= 596/sqrtX
delta bpm=-1/2 * 596/xsqrtx= -1/2 * 596*bpm/height * dheight
deltabpm= -298*bpm*1/60=-5*bpm
To estimate the change in pulse rate corresponding to a height change, we can use linear approximation. Linear approximation involves finding the slope of a tangent line to the curve at a specific point and using that slope to approximate changes in one variable based on changes in another variable.
In this case, we want to estimate the change in pulse rate with a height change from 59 inches to 60 inches.
First, let's find the formula for average pulse rate as a function of height. The given formula is 596/(x^0.5), where x represents the height in inches.
To find the slope at a specific point, we need to take the derivative of the average pulse rate function with respect to height. Taking the derivative of the given formula gives us:
dP/dx = -298/(x^1.5)
Now, let's find the slope at the height of 59 inches. Plug in x = 59 into the derivative:
dP/dx = -298/(59^1.5)
Calculate this to get the slope at the height of 59 inches.
Next, we need to use the slope to approximate the change in pulse rate. Since we've already found the slope, we can use the formula for linear approximation:
ΔP ≈ slope * Δx
where ΔP represents the change in pulse rate, slope is the calculated slope at the specific height, and Δx is the change in height.
In this case, the change in height is from 59 inches to 60 inches, so Δx = 60 - 59 = 1 inch.
Now, multiply the slope we calculated earlier with Δx to find the estimated change in pulse rate:
ΔP ≈ slope * Δx
Substitute the slope value and Δx value into the formula to get the estimated change in pulse rate.