The Growth Decay Calculator is designed to facilitate quick and accurate predictions for scenarios exhibiting exponential growth or decay. Whether you are calculating compound interest, population growth, or radioactive decay, this tool ensures that you have the precise figures needed for informed decision-making.
Formula of Growth Decay Calculator
Exponential Growth Formula:
The formula used for calculating exponential growth is:
where:
- f(t) represents the value at time t
- a is the initial quantity when t = 0
- r is the growth rate, expressed as a decimal (e.g., 0.05 for 5% growth)
- t indicates the time period
This formula is pivotal in scenarios such as calculating continuous compound interest or projected increases in population under consistent growth conditions.
Exponential Decay Formula:
Conversely, the formula for exponential decay is outlined as:
with the components:
- f(t) as the value at time t
- a as the starting quantity at t = 0
- r as the decay rate, presented as a negative decimal to indicate reduction
- t as the duration of decay
This model is essential for understanding processes like radioactive decay or depreciation of assets over time.
Pre-Calculated Tables for Common Terms
Table 1: Exponential Growth Rates
| Time (Years) | 3% Growth Rate (r=0.03) | 5% Growth Rate (r=0.05) | 7% Growth Rate (r=0.07) |
|---|---|---|---|
| 1 | 103.00 | 105.00 | 107.00 |
| 2 | 106.09 | 110.25 | 114.49 |
| 3 | 109.27 | 115.76 | 122.50 |
| 4 | 112.55 | 121.55 | 131.08 |
| 5 | 115.93 | 127.63 | 140.26 |
Table 2: Exponential Decay Rates
| Time (Years) | 3% Decay Rate (r=−0.03) | 5% Decay Rate (r=−0.05) | 7% Decay Rate (r=−0.07) |
|---|---|---|---|
| 1 | 97.00 | 95.00 | 93.00 |
| 2 | 94.09 | 90.25 | 86.49 |
| 3 | 91.26 | 85.74 | 80.44 |
| 4 | 88.52 | 81.45 | 74.81 |
| 5 | 85.86 | 77.38 | 69.58 |
Example of Growth Decay Calculator
Growth Example: If an initial amount of 100 units grows at 5% per year, the amount after 3 years can be calculated as: f(3) = 100(1 + 0.05)^3 = 115.76 units
Decay Example: If an initial amount of 100 units decays at 5% per year, the amount after 3 years can be calculated as: f(3) = 100(1 – 0.05)^3 = 85.74 units
Most Common FAQs
The calculator uses standard mathematical formulas for exponential growth and decay, ensuring high accuracy when the correct inputs are provided. Users should verify their input values for the best results.
This calculator is specifically designed for exponential models. For other types of mathematical predictions, such as linear or logistic growth, additional tools and methods would be more appropriate.
Ensure that all input values are correct, particularly the rate of growth or decay, which should be entered as a decimal. Recalculate as needed and consult additional resources if discrepancies continue.