Question

the function below represents the amount of radioactive substance, in grams, remaining in the area after a given time, in days. decay of a radioactive substance the average rate of change in the remaining radioactive substance as the time increases from day 2 to day 4 is

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 4$, and the function represents the amount of radioactive substance $y$ with respect to time $x$ (in days).

Step2: Estimate function values from the graph

From the graph, when $x = 2$, the amount of radioactive substance $y_1\approx30$ grams, and when $x = 4$, the amount of radioactive substance $y_2\approx15$ grams.

Step3: Calculate the average rate of change

Using the formula $\frac{y_2 - y_1}{4 - 2}=\frac{15 - 30}{2}=\frac{- 15}{2}=-7.5$ grams per day.

Answer:

$-7.5$