the table below shows the average weight of a type of plankton after several weeks.\n| time (weeks) | weight…
the table below shows the average weight of a type of plankton after several weeks.\n| time (weeks) | weight (ounces) |\n| ---- | ---- |\n| 8 | 0.04 |\n| 9 | 0.07 |\n| 10 | 0.14 |\n| 11 | 0.25 |\n| 12 | 0.49 |\nwhat is the average rate of change in weight of the plankton from week 8 to week 12?\na 0.0265 ounce per week\nb 0.0375 ounce per week\nc 0.055 ounce per week\nd 0.1125 ounce per week
Answer
Explanation:
Step1: Identify the formula for average rate of change
The formula for the average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x$ is time (weeks) and $y$ is weight (ounces). $x_1 = 8$, $y_1=0.04$, $x_2 = 12$, $y_2 = 0.49$.
Step2: Substitute values into the formula
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{0.49 - 0.04}{12 - 8}$.
Step3: Calculate the numerator and denominator
The numerator is $0.49-0.04 = 0.45$, and the denominator is $12 - 8=4$.
Step4: Calculate the average rate of change
$\frac{0.45}{4}=0.1125$ ounce per week.
Answer:
D. 0.1125 ounce per week