find the relative rate of change of f(x)=15 + 7 ln x.\nthe relative rate of change of f(x) is \n

Explanation:

Step1: Recall the formula for relative rate of change

The relative rate of change of a function $y = f(x)$ is given by $\frac{f'(x)}{f(x)}$. First, find the derivative of $f(x)=15 + 7\ln x$. The derivative of a constant is 0 and the derivative of $\ln x$ is $\frac{1}{x}$. So, $f'(x)=\frac{7}{x}$.

Step2: Calculate the relative rate of change

Substitute $f(x)$ and $f'(x)$ into the relative - rate - of - change formula. We have $\frac{f'(x)}{f(x)}=\frac{\frac{7}{x}}{15 + 7\ln x}=\frac{7}{x(15 + 7\ln x)}$.

Answer:

$\frac{7}{x(15 + 7\ln x)}$