6.2.3
Graphing Linear and Exponential Growth
Drawing Graphs of Exponential Growth and Decay
Drawing Graphs of Exponential Growth and Decay
Exponential growth and decay can be plotted on a graph.
![Illustrative background for From a multiplier to a graph](https://image-v2.cdn.app.senecalearning.com/2019-04/14953829-e62c-42a2-985a-3131db5a54fe/multiply-times,h_400,q_80,w_640.jpg)
![Illustrative background for From a multiplier to a graph ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-04/14953829-e62c-42a2-985a-3131db5a54fe/multiply-times,h_400,q_80,w_640.jpg)
From a multiplier to a graph
From a multiplier to a graph
- A multiplier for exponential growth or decay can be used to generate a table of values.
- A graph can then be plotted from the table of values.
![Illustrative background for Example question](https://image-v2.cdn.app.senecalearning.com/2018-09/80e8f9c4-8278-4f7c-9cee-406a6078a0ac/pathogen-cell-bacteria-antigens,h_400,q_80,w_640.jpg)
![Illustrative background for Example question ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-09/80e8f9c4-8278-4f7c-9cee-406a6078a0ac/pathogen-cell-bacteria-antigens,h_400,q_80,w_640.jpg)
Example question
Example question
- The population of a colony of bacteria increases by 2× every 2 weeks. The colony has a population of 50 at week 0.
- Plot a graph showing the exponential growth of the population.
![Illustrative background for Example answer](https://image-v2.cdn.app.senecalearning.com/2019-04/bdc6fe81-f7dc-4048-ba21-5703e6bd4844/New%20wave%201.4,h_400,q_80,w_640.png)
![Illustrative background for Example answer ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-04/bdc6fe81-f7dc-4048-ba21-5703e6bd4844/New%20wave%201.4,h_400,q_80,w_640.png)
Example answer
Example answer
- Generate a table of values.
- shows the number of weeks.
- shows the population size.
![Illustrative background for Example answer cont.](https://image-v2.cdn.app.senecalearning.com/2019-04/0ee59788-9726-4a7c-af2e-3945d365e949/exponential-growth-graph-population-bacteria,h_400,q_80,w_640.png)
![Illustrative background for Example answer cont. ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-04/0ee59788-9726-4a7c-af2e-3945d365e949/exponential-growth-graph-population-bacteria,h_400,q_80,w_640.png)
Example answer cont.
Example answer cont.
- Plot these values on a graph.
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
Jump to other topics
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
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