Digital SATMath: Problem-Solving and Data AnalysisEasy
A botanist is studying the growth of a rare plant. She observes that the plant's height increases by 1.5 cm every 3 days. If the plant is initially 12 cm tall, what will its height be after 18 days?
- A21 cm
- B18 cm
- C15 cm
- D24 cm
Show answer & explanationAnswer & explanation
Correct answer: A. 21 cm
The plant grows 1.5 cm every 3 days, which is 0.5 cm per day. Over 18 days, it will grow 0.5 cm/day * 18 days = 9 cm. Adding this to the initial height of 12 cm gives 21 cm.
Why the other options are wrong
- B. This option might result from incorrectly calculating the total growth (e.g., 18 days / 3 days = 6 growth periods, but then multiplying by 1 cm instead of 1.5 cm, then adding to initial height).
- C. This option results from only adding 3 times the growth rate (1.5 cm * 3 = 4.5 cm) to the initial height, not considering the full 18 days.
- D. This option might result from an overestimation of the growth or a calculation error such as multiplying 1.5 cm by 6 and then adding 12 cm, but miscalculating the total.
Constant Rate of Change
A constant rate of change means that a quantity increases or decreases by the same amount over equal intervals of time or other independent variable.
- Can be represented by a linear function.
- The slope of the line represents the rate of change.
- Often involves calculating total change over a period.
Memory trick: Rate times Time equals Total Change, then add to Start.