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The Power of Doubling

Part of Exponential Graphs · GCSE GCSE Mathematics revision

This introduction covers The Power of Doubling 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 1 of 10 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 10

Practice

11 questions

Recall

10 flashcards

The Power of Doubling

An ancient legend tells of a chess player who asked a king for one grain of rice on the first square, two on the second, four on the third — doubling each time. The king agreed, thinking it a small reward. By square 64, the total would be 18 billion billion grains — more than all the rice ever grown. That is exponential growth: slow at first, then exploding. It describes population growth, compound interest, radioactive decay, and the spread of diseases — all from the deceptively simple equation y = aˣ.

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 EssentialsExponential Growth vs DecayKey Features of Exponential Graphs

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).

11 questions on Exponential Graphs — practise free

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Exponential Graph Essentials