Question

a research group using hospital records developed an approximate mathematical model relating systolic blood pressure and age. p(x)=60 + 35 ln(x + 2) 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 10 years is 2.92 mm/year. (type an integer or decimal rounded to the nearest hundredth as needed.) the rate of change of pressure at the end of 30 years is mm/year. (type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Find the derivative of $P(x)$

The derivative of $P(x)=60 + 35\ln(x + 2)$ using the rule $\frac{d}{dx}\ln(u)=\frac{u'}{u}$ where $u=x + 2$ and $u'=1$. So $P'(x)=\frac{35}{x + 2}$.

Step2: Evaluate $P'(x)$ at $x = 30$

Substitute $x = 30$ into $P'(x)$. We get $P'(30)=\frac{35}{30+ 2}=\frac{35}{32}=1.09375$.

Step3: Round the result

Rounding $1.09375$ to the nearest hundred - th gives $1.09$.

Answer:

$1.09$