The Koru Calculator helps users understand and predict the growth of the Koru plant, which is significant in various cultures, particularly in New Zealand. The Koru is known for its spiral shape symbolizing new life, growth, strength, and peace.
Inputs
- Initial Diameter (ID): The initial diameter of the Koru spiral, measured in centimeters or inches.
- Growth Rate (GR): The percentage growth rate per time period (e.g., monthly growth rate).
- Time Periods (T): The number of time periods over which the growth is calculated (e.g., number of months).
Formulas and Calculations
1. Calculate the Diameter after Growth
The growth of the Koru can be modeled using exponential growth, given by the formula:
[ D_t = ID \times (1 + \frac{GR}{100})^T ]
where:
- ( D_t ) = Diameter after time period ( T )
- ( ID ) = Initial Diameter
- ( GR ) = Growth Rate (percentage)
- ( T ) = Number of time periods
Example Calculation
Inputs:
- Initial Diameter (ID): 10 cm
- Growth Rate (GR): 5% per month
- Time Periods (T): 12 months
- Calculate the Diameter after Growth:
[ D_t = 10 \times (1 + \frac{5}{100})^{12} ]
[ D_t = 10 \times (1 + 0.05)^{12} ]
[ D_t = 10 \times (1.05)^{12} ]
[ D_t \approx 10 \times 1.795856 ]
[ D_t \approx 17.96 \text{ cm} ]
Summary
For a Koru plant with an initial diameter of 10 cm and a growth rate of 5% per month, the diameter after 12 months is approximately 17.96 cm.
Relevant Information Table
| Input Parameters | Values |
|---|---|
| Initial Diameter | 10 cm |
| Growth Rate | 5% per month |
| Time Periods | 12 months |
| Final Diameter | 17.96 cm (approx.) |
Conclusion
The Koru Calculator is a valuable tool for anyone interested in understanding the growth patterns of the Koru plant. By providing accurate predictions based on initial size, growth rate, and time periods, this calculator helps users appreciate the plant’s development and its cultural significance.