This topic summary covers Topic Summary: Exponential Graphs within Exponential Graphs for GCSE Mathematics. Revise Exponential Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 10 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
11 questions
Recall
10 flashcards
Topic Summary: Exponential Graphs
Key Facts
- y = aˣ: y-intercept always (0, 1)
- Asymptote: y = 0 (never crosses x-axis)
- y always positive
- Growth: a > 1; Decay: 0 < a < 1
- y = k × aˣ: y-intercept is (0, k)
Real-Life Formulas
- Compound interest: A = P(1 + r/100)ⁿ
- Depreciation: V = P(1 − r/100)ⁿ
- Growth multiplier: (1 + r/100)
- Decay multiplier: (1 − r/100)
Key Vocabulary
- Exponential growth: multiplies by a fixed ratio > 1 each period
- Exponential decay: multiplies by a ratio between 0 and 1
- Asymptote: line the curve approaches but never reaches
- Base (a): the constant being raised to a power
Common Errors
- Thinking y-intercept is (0, 0) instead of (0, 1)
- Allowing the decay curve to touch the x-axis
- Confusing exponential growth with linear growth
- Using wrong multiplier in compound interest formula