Q10.4: The rate of change of pressure at the end of 20 years is _______ ​mm/year. ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

Question

A research group using hospital records developed an approximate mathematical model relating systolic blood pressure and age.

P(x)=50+25ln(x+3) 0≤x≤65

​P(x) is pressure measured in millimeters of mercury and x is age in years.

The rate of change of pressure at the end of 20 years is _______ ​mm/year.

​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

Answer 1

To get the rate of change in blood pressure, need to take the derivative of P(x).

P'(x) = 25/(x+3)

P'(20) = 25/23 = 1.09 mm/year

Answer 2

Hello, Jerry,

I'm a little out of my element here, so please read accordingly. (I'm a chemist, so "out of my element" is the start of a horror story).

We're looking for the "rate of change" in the blood pressure of individuals in the 20 year age group. This suggests we take the first derivative of the equation describing pressure as a function of age. That would give us the slope of the original equation at any time x years.

I believe the first derivative of y = 50 + 25*ln(x+3) would be:

d/d(20) = 25/(20+3) = 34.04 mmHg/year

Please decide on your own if this makes sense. Perhaps someone could correct me if I differentiated incorrectly.

Bob