Interpreting Exponential Growth and Decay Graphs
Maths: Edexcel A Level Pure Maths, topic 6.2.4
Interpreting Exponential Growth and Decay Graphs
Exponential growth and decay graphs can be used to gather data about the growth or decay.
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.
Example
- After 2 years the car is worth approximately $4,900.
- After 6 years the car is worth approximately $1,200.
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.
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.
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
Multiplier example cont.
- Find the average of the values:
- (0.704 + 0.696 + 0.708) ÷ 3 = 0.703 (3 d.p.)
Test yourself on Interpreting Exponential Growth and Decay Graphs
The value of a car decays exponentially by a fixed multiplier each year. The car is valued at $7,000 at year 1 and $5,000 at year 2. What is the multiplier for this exponential decay?
The value of a remote-controlled plane decays exponentially by a fixed multiplier each year. The car is valued at $7,000 at year 1 and $5,000 at year 2. What is the multiplier for this exponential decay?
The value of a phone decays exponentially by a fixed multiplier each month. The phone is valued at $800 when it is new and $560 when it is 1 year old. What is the multiplier for this exponential decay?
The value of a phone decays exponentially by a fixed multiplier each month. The phone is valued at $1,100 when it is new and $700 when it is 1 year old. What is the multiplier for this exponential decay?