Exponential Growth and Decay in Real Life

Part of Exponential Graphs · Section 5 of 10

Deep DiveUnit: GraphsGCSE

This deep dive covers Exponential Growth and Decay in Real Life 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 5 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Exponential Growth and Decay in Real Life

Compound Interest (Growth)

A = P(1 + r/100)ⁿ

Where A = final amount, P = principal, r = annual rate (%), n = number of years.

Example: £1000 invested at 5% per year for 10 years.

A = 1000 × (1.05)¹⁰ = 1000 × 1.629 ≈ £1629

Depreciation (Decay)

V = P(1 − r/100)ⁿ

Where V = final value, P = initial value, r = % decrease per period.

Example: Car worth £12,000 depreciates 15% per year. Value after 5 years:

V = 12000 × (0.85)⁵ = 12000 × 0.444 ≈ £5325

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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