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Worked Examples

Part of Exponential Graphs · GCSE GCSE Mathematics revision

This study notes covers Worked Examples 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 8 of 10 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 8 of 10

Practice

11 questions

Recall

10 flashcards

✏️ Worked Examples

Example 1: Drawing an Exponential Graph

Question: Complete the table of values for y = 2ˣ for x = -2, -1, 0, 1, 2, 3. State the y-intercept and describe the asymptote.

Show Solution

Calculate y for each x value:

x = -2: y = 2⁻² = 1/4 = 0.25    x = -1: y = 2⁻¹ = 0.5

x = 0: y = 2⁰ = 1    x = 1: y = 2¹ = 2    x = 2: y = 2² = 4    x = 3: y = 2³ = 8

y-intercept: (0, 1) — since 2⁰ = 1 for any base

Asymptote: y = 0 (the x-axis) — as x → -∞, y approaches 0 but never reaches it

Shape: Growth curve (a = 2 > 1) — rises steeply to the right, approaches the x-axis to the left.

Answer: y values: 0.25, 0.5, 1, 2, 4, 8. y-intercept at (0, 1). Asymptote: y = 0.

Example 2: Exponential Growth — Compound Interest

Question: £500 is invested at 4% per year compound interest. How much is it worth after 3 years?

Show Solution

Step 1: Identify the formula — A = P(1 + r/100)ⁿ

Step 2: Identify values — P = 500, r = 4, n = 3

Step 3: Calculate the multiplier — 1 + 4/100 = 1.04

Step 4: Calculate A — A = 500 × (1.04)³ = 500 × 1.124864 ≈ £562.43

Answer: £562.43 (to the nearest penny)

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.

Exam Tips for Exponential GraphsCommon MisconceptionsThe Power of DoublingExponential 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