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Exponential Growth vs Decay

Part of Exponential Graphs — GCSE Mathematics

This diagram covers Exponential Growth vs Decay 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 3 of 10 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.

Topic position

Section 3 of 10

Practice

11 questions

Recall

10 flashcards

Exponential Growth vs Decay

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.

Exponential Graph Essentials Key Features of Exponential Graphs The Power of Doubling Exponential Growth and Decay in Real Life

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 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.

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).

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Exponential Graph Essentials

Key Features of Exponential Graphs