GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A biologist is studying the growth of a plant. She records the plant's height in centimeters over several weeks. At week 2, the plant was 10 cm tall. At week 6, the plant was 22 cm tall. Assuming the growth is linear, what was the average rate of growth of the plant in centimeters per week?
- A3 cm/week
- B4 cm/week
- C6 cm/week
- D2 cm/week
Show answer & explanationAnswer & explanation
Correct answer: A. 3 cm/week
The average rate of growth is equivalent to the slope of the line connecting the two given points. Calculate the change in height divided by the change in weeks to find the rate.
Why the other options are wrong
- B. This is incorrect; it might result from an arithmetic error in calculating the differences.
- C. This is incorrect; it represents the total change in height, not the rate of change.
- D. This is incorrect; it might result from dividing the change in height by an incorrect change in time.
Average Rate of Change
The average rate of change of a function over an interval is the slope of the secant line connecting the two endpoints of the interval.
- Calculated as (change in y) / (change in x)
- Represents how much one quantity changes, on average, per unit change in another quantity
- For linear functions, it is constant and equal to the slope
Memory trick: Rate is Rise over Run, always remember the slope!