12 the table below shows the average diameter...
12 the table below shows the average diameter of a pupil in a persons eye as he or she grows older. what is the average rate of change, in millimeters per year, of a persons pupil diameter from age 20 to age 80? 1) 2.4 2) 0.04 3) -2.4 4) -0.04
Answer
# Explanation:
## Step1: Identify the formula for average rate of change
The formula for the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x$ is age and $y$ is the average pupil - diameter. Let $x_1 = 20$, $y_1=4.7$, $x_2 = 80$, and $y_2 = 2.3$.
## Step2: Substitute values into the formula
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{2.3 - 4.7}{80 - 20}$.
## Step3: Calculate the numerator and denominator
The numerator is $2.3−4.7=-2.4$, and the denominator is $80 - 20 = 60$.
## Step4: Calculate the average rate of change
$\frac{-2.4}{60}=-0.04$.
# Answer:
4) - 0.04