Question

the electromagnetic force between two particular particles is related to the distance between the particles. this relationship is modeled by the function f, where f(d) = \frac{3.6}{d^{2}} for distance d, measured in centimeters, and force f(d), measured in newtons. what is the average rate of change, in newtons per centimeter, in the electromagnetic force if the distance between two particles is increased from 2.3 centimeters to 3.1 centimeters?
(a) -0.382
(b) -0.306
(c) 0.375
(d) 5.625

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = F(d)$ from $d = a$ to $d = b$ is $\frac{F(b)-F(a)}{b - a}$. Here, $a = 2.3$, $b=3.1$, and $F(d)=\frac{3.6}{d^{2}}$.

Step2: Calculate $F(2.3)$

$F(2.3)=\frac{3.6}{(2.3)^{2}}=\frac{3.6}{5.29}\approx0.6805$.

Step3: Calculate $F(3.1)$

$F(3.1)=\frac{3.6}{(3.1)^{2}}=\frac{3.6}{9.61}\approx0.3746$.

Step4: Calculate average rate of change

$\frac{F(3.1)-F(2.3)}{3.1 - 2.3}=\frac{0.3746 - 0.6805}{0.8}=\frac{- 0.3059}{0.8}\approx - 0.382$.

Answer:

A. -0.382