Question

at the start of summer vacation, wesley decides to learn a number of kanji characters each week. the total number of characters wesley knows, y, is a function of the number of weeks, x. the graph of the function passes through the points (3, 120) and (5, 160).

1. find and describe the rate of change of the function.
2. the rate of change is ?. it represents the number of characters wesley learns ? each week in all

Explanation:

Step1: Define rate of change formula

The rate of change between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$.

Step2: Substitute given points

Substitute $(3,120)$ and $(5,160)$:
$\frac{160-120}{5-3} = \frac{40}{2} = 20$

Step3: Interpret the rate

The rate is the weekly character count.

Answer:

The rate of change is $20$. It represents the number of characters Wesley learns 20 each week.