6.2.4
Interpreting Exponential Growth and Decay Graphs
Interpreting Exponential Growth and Decay Graphs
Interpreting Exponential Growth and Decay Graphs
Exponential growth and decay graphs can be used to gather data about the growth or decay.
![Illustrative background for Estimating values](https://image-v2.cdn.app.senecalearning.com/2019-08/8a00fd63-c963-4c6a-84ad-5c07275e668e/Screen%20Shot%202019-08-05%20at%203.56.09%20pm,h_400,q_80,w_640.png)
![Illustrative background for Estimating values ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-08/8a00fd63-c963-4c6a-84ad-5c07275e668e/Screen%20Shot%202019-08-05%20at%203.56.09%20pm,h_400,q_80,w_640.png)
Estimating values
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.
![Illustrative background for Example](https://image-v2.cdn.app.senecalearning.com/2019-08/38a072f8-70eb-4958-9dc8-433bc0a2a47b/Screen%20Shot%202019-08-05%20at%204.05.12%20pm,h_400,q_80,w_640.png)
![Illustrative background for Example ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-08/38a072f8-70eb-4958-9dc8-433bc0a2a47b/Screen%20Shot%202019-08-05%20at%204.05.12%20pm,h_400,q_80,w_640.png)
Example
Example
- After 2 years the car is worth approximately $4,900.
- After 6 years the car is worth approximately $1,200.
![Illustrative background for Finding the multiplier](https://image-v2.cdn.app.senecalearning.com/2019-08/8a00fd63-c963-4c6a-84ad-5c07275e668e/Screen%20Shot%202019-08-05%20at%203.56.09%20pm,h_400,q_80,w_640.png)
![Illustrative background for Finding the multiplier ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-08/8a00fd63-c963-4c6a-84ad-5c07275e668e/Screen%20Shot%202019-08-05%20at%203.56.09%20pm,h_400,q_80,w_640.png)
Finding the multiplier
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.
![Illustrative background for Multiplier example](https://image-v2.cdn.app.senecalearning.com/2019-08/d33e0029-969d-4771-94d0-87fb2f9d65b2/Screen%20Shot%202019-08-05%20at%204.08.02%20pm,h_400,q_80,w_640.png)
![Illustrative background for Multiplier example ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-08/d33e0029-969d-4771-94d0-87fb2f9d65b2/Screen%20Shot%202019-08-05%20at%204.08.02%20pm,h_400,q_80,w_640.png)
Multiplier example
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.
![Illustrative background for Multiplier example cont.](https://image-v2.cdn.app.senecalearning.com/2019-08/d33e0029-969d-4771-94d0-87fb2f9d65b2/Screen%20Shot%202019-08-05%20at%204.08.02%20pm,h_400,q_80,w_640.png)
![Illustrative background for Multiplier example cont. ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-08/d33e0029-969d-4771-94d0-87fb2f9d65b2/Screen%20Shot%202019-08-05%20at%204.08.02%20pm,h_400,q_80,w_640.png)
Multiplier example cont.
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
![Illustrative background for Multiplier example cont.](https://image-v2.cdn.app.senecalearning.com/2019-08/d33e0029-969d-4771-94d0-87fb2f9d65b2/Screen%20Shot%202019-08-05%20at%204.08.02%20pm,h_400,q_80,w_640.png)
![Illustrative background for Multiplier example cont. ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-08/d33e0029-969d-4771-94d0-87fb2f9d65b2/Screen%20Shot%202019-08-05%20at%204.08.02%20pm,h_400,q_80,w_640.png)
Multiplier example cont.
Multiplier example cont.
- Find the average of the values:
- (0.704 + 0.696 + 0.708) ÷ 3 = 0.703 (3 d.p.)
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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