Problem-Solving and Data AnalysisMediumRecognising exponential growth
Problem-Solving and Data Analysis practice question
A quantity increases by 5% every year. Which type of function best models the quantity over time, and why?
- A. Exponential, because the quantity is multiplied by the same factor (1.05) each year.Correct
- B. Linear, because the quantity increases by the same amount each year.
- C. Linear, because 5% is a constant.
- D. Quadratic, because the increase gets larger each year.
Answer: A. Exponential, because the quantity is multiplied by the same factor (1.05) each year.
A percent increase multiplies the current amount by 1.05 every year — a constant factor, which is exponential growth.
Why the other answers are wrong
- B. Linear, because the quantity increases by the same amount each year.
- The AMOUNT added grows each year (5% of a larger number), so it isn't a constant amount.
- C. Linear, because 5% is a constant.
- The percent is constant, but a constant percent means a constant FACTOR, not a constant amount — that's exponential.
- D. Quadratic, because the increase gets larger each year.
- The increase does grow, but by a constant ratio, which is exponential, not quadratic.
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