6.2.4

Interpreting Exponential Growth and Decay Graphs

Test yourself

Interpreting Exponential Growth and Decay Graphs

Exponential growth and decay graphs can be used to gather data about the growth or decay.

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Estimating values

  • You can use a graph to estimate values.
    • The graph shows the value of a car over an 8 year period. Estimate how much the car is worth after 2 years and after 6 years.
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Example

  • After 2 years the car is worth approximately $4,900.
  • After 6 years the car is worth approximately $1,200.
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Finding the multiplier

  • You can also use a graph to find out the rate of growth/decay.
  • You can do this by looking at the multiplier between consecutive values in the data.
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Multiplier example

  • Find values at consecutive time intervals:
    • After 2 years the value is approximately $4,900.
    • After 3 years the value is approximately $3,450.
    • After 4 years the value is approximately $2,400.
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Multiplier example cont.

  • Find the multiplier between each of the consecutive values:
    • $3,450 ÷ $4,900 = 0.704
    • $2,400 ÷ $3,450 = 0.696
    • $1,700 ÷ $2,400 = 0.708
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Multiplier example cont.

  • Find the average of the values:
    • (0.704 + 0.696 + 0.708) ÷ 3 = 0.703 (3 d.p.)

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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