š Exponential Growth Calculator
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š Understanding Exponential Growth
Exponential growth occurs when a quantity increases at a constant rate over time. The general formula is:
- P = Pā * e^(rt)
- Where:
- P = Final amount
- Pā = Initial amount
- r = Growth rate (as a decimal)
- t = Time
š Example Calculations
| Initial Value (Pā) | Growth Rate (r) | Time (t) | Final Value (P) |
|---|---|---|---|
| 1000 | 5% | 3 years | 1161.83 |
| 500 | 10% | 2 years | 610.70 |
š§ Practical Applications of Exponential Growth
1. Finance & Economics: Used in compound interest and investment growth.
2. Biology & Medicine: Helps in modeling population growth and bacterial growth.
3. Physics & Engineering: Essential in decay rates and reaction processes.
ā FAQs
Q1: How do I calculate exponential growth?
ā
Use the formula P = Pā * e^(rt).
Q2: What does ‘e’ represent?
ā
‘e’ is the mathematical constant (approximately 2.718), used in exponential functions.
Q3: How is exponential growth different from linear growth?
ā
Exponential growth increases at a rate proportional to its current value, while linear growth increases by a fixed amount.
Q4: Where is exponential growth commonly used?
ā
It is widely used in **finance, biology, and physics**.
Q5: Why is exponential growth important?
ā
It helps in **understanding rapid changes in populations, investments, and scientific processes**.