Question

a research group using hospital records developed an approximate mathematical model relating systolic blood pressure and age. $p(x)=60 + 35ln(x + 2)$ $0leq xleq65$ $p(x)$ 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 $square$ mm/year. (type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Find the derivative of P(x)

We know that if $P(x)=60 + 35\ln(x + 2)$, using the derivative formula for $\ln(u)$ where $u=x + 2$ and $\frac{d}{dx}\ln(u)=\frac{u'}{u}$. The derivative of a constant is 0, and the derivative of $35\ln(x + 2)$ is $35\times\frac{1}{x + 2}$. So $P'(x)=\frac{35}{x + 2}$.

Step2: Evaluate P'(x) at x = 10

Substitute $x = 10$ into $P'(x)$. We get $P'(10)=\frac{35}{10+ 2}=\frac{35}{12}\approx2.92$.

Answer:

$2.92$