GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A biologist is studying the growth of a plant. She records the plant's height in centimeters over several weeks. If the plant grows from 10 cm to 25 cm in 5 weeks, what is the average rate of change of the plant's height per week?
- A3 cm/week
- B5 cm/week
- C15 cm/week
- D2 cm/week
Show answer & explanationAnswer & explanation
Correct answer: A. 3 cm/week
The average rate of change is calculated as the change in the dependent variable (height) divided by the change in the independent variable (time). Change in height = 25 cm - 10 cm = 15 cm. Change in time = 5 weeks. Average rate of change = 15 cm / 5 weeks = 3 cm/week.
Why the other options are wrong
- B. This is the number of weeks, not the rate of change.
- C. This is the total change in height, not the rate of change per week.
- D. This would be the result if the height change was 10cm or if the time was 7.5 weeks.
Slope as Average Rate of Change
The slope of a line represents the average rate of change of the dependent variable with respect to the independent variable over an interval. It's calculated as the ratio of the change in y to the change in x.
- Formula: Average Rate of Change = (Change in Y) / (Change in X).
- Similar to the slope formula (y2 - y1) / (x2 - x1).
- Units are typically 'units of Y per unit of X'.
- For non-linear functions, it's the slope of the secant line between two points.
Memory trick: Rate of Change is 'Rise over Run' between two points, like a slope!