Question

the financial aid office at clayton university produced an internal report on the number of students receiving scholarships. students receiving scholarships according to the graph, when was the rate of change greater? between 2023 and 2024 between 2022 and 2025

Explanation:

Step1: Recall rate - of - change formula

The rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ represents the number of students and $x$ represents the year.

Step2: Calculate rate of change between 2023 and 2024

In 2023, the number of students $y_1 = 75$, and in 2024, $y_2 = 85$. $\Delta y=85 - 75 = 10$, $\Delta x=2024 - 2023 = 1$. Rate of change $r_1=\frac{85 - 75}{2024 - 2023}=10$.

Step3: Calculate rate of change between 2022 and 2025

In 2022, $y_1 = 40$, and in 2025, $y_2 = 75$. $\Delta y=75 - 40 = 35$, $\Delta x=2025 - 2022 = 3$. Rate of change $r_2=\frac{75 - 40}{2025 - 2022}=\frac{35}{3}\approx11.67$.

Answer:

between 2022 and 2025