consider the graph of ( f(x) ), which represents the total area, in square feet, of a fungus growing in a…

consider the graph of ( f(x) ), which represents the total area, in square feet, of a fungus growing in a particular location ( x ) days after the initial area of the fungus. what is the approximate average rate of change of the function from ( x = 0 ) to ( x = 3 )? 2 square feet per day 3 square feet per day 12 square feet per day 13 square feet per day

consider the graph of ( f(x) ), which represents the total area, in square feet, of a fungus growing in a particular location ( x ) days after the initial area of the fungus. what is the approximate average rate of change of the function from ( x = 0 ) to ( x = 3 )? 2 square feet per day 3 square feet per day 12 square feet per day 13 square feet per day

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$.

Step2: Identify $a$, $b$, $f(a)$ and $f(b)$

Here, $a = 0$, $b=3$. From the graph, when $x = 0$, $f(0)=5$ (the $y$-intercept), and when $x = 3$, $f(3)=40$.

Step3: Calculate the average rate of change

Substitute the values into the formula: $\frac{f(3)-f(0)}{3 - 0}=\frac{40 - 5}{3}=\frac{35}{3}\approx12$ square feet per day.

Answer:

12 square feet per day