GraphsTopic Summary

Knowledge Organiser: Exponential Graphs

Part of Exponential Graphs · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: 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

Knowledge Organiser: 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

Key Formulas

Growth: y = a × bˣ where b > 1
Decay: y = a × bˣ where 0 < b < 1
y-intercept always at (0, a) — substitute x = 0
Asymptote: y = 0 (x-axis) — curve approaches but never touches

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Keep building this topic

Read this section alongside the surrounding pages in Exponential Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Common Misconceptions The Power of Doubling Exponential Graph Essentials

Practice Questions for Exponential Graphs

The graph of y = 3ˣ always passes through which point?

A. (0, 0)
B. (0, 1)
C. (1, 0)
D. (3, 0)

1 markfoundation

Explain why the graph of y = 3ˣ has a horizontal asymptote at y = 0, and state the domain of values that y can take.

2 markshigher

Quick Recall Flashcards

What is the y-intercept of any graph y = aˣ?

The y-intercept is always (0, 1). Reason: when x = 0, y = a⁰ = 1 for any base a. This is true for y = 2ˣ, y = 3ˣ, y = 5ˣ, and even y = (0.5)ˣ. All exponential graphs of the form y = aˣ pass through (0, 1).

What is the asymptote of y = aˣ?

The x-axis (the line y = 0) is a horizontal asymptote. For growth (a > 1): as x → -∞, y → 0 but never reaches 0 For decay (0 < a < 1): as x → +∞, y → 0 but never reaches 0 The graph gets infinitely close to the x-axis but never crosses it. y is always positive — it never equals zero.

11 questions on Exponential Graphs — practise free

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Common Misconceptions

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Exponential Graphs