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)