find the percentage rate of change of f(x) at the indicated value of x. f(x)=210 + 85x; x = 4 the percentage…

Explanation:

Step1: Find the derivative of f(x)

The derivative of $f(x)=210 + 85x$ with respect to $x$ is $f^\prime(x)=\frac{d}{dx}(210)+\frac{d}{dx}(85x)$. Since the derivative of a constant $\frac{d}{dx}(210) = 0$ and $\frac{d}{dx}(ax)=a$ for a constant $a$, we have $f^\prime(x)=85$.

Step2: Calculate f(4)

Substitute $x = 4$ into $f(x)$: $f(4)=210+85\times4=210 + 340=550$.

Step3: Calculate the percentage rate of change

The percentage rate of change of a function $y = f(x)$ at a point $x$ is given by $\frac{f^\prime(x)}{f(x)}\times100%$. Substitute $f^\prime(4) = 85$ and $f(4)=550$ into the formula: $\frac{85}{550}\times100%=\frac{8500}{550}% \approx 15.5%$.

Answer:

$15.5$