Write the Equation of an Exponential Function Calculator
Introduction & Importance
Exponential functions are ubiquitous in mathematics, physics, economics, and many other fields. Understanding and being able to write their equations is crucial…
How to Use This Calculator
- Enter the base (a), growth rate (r), and time (t) values.
- Click ‘Calculate’.
- View the result and chart.
Formula & Methodology
The formula for an exponential function is: A(t) = a * e^(rt), where…
Real-World Examples
Example 1: If a population grows at a rate of 3% per year, and the initial population is 100,000, what will the population be in 10 years?
Example 2: If an investment grows at an annual rate of 8%, and the initial investment is $10,000, what will the investment be worth in 5 years?
Example 3: If a radioactive substance decays at a rate of 2% per year, and the initial amount is 100 grams, how much will be left after 20 years?
Data & Statistics
| Organism/Process | Growth Rate (r) |
|---|---|
| Bacteria (E. coli) | 0.5 – 1 per hour |
| Yeast | 0.2 – 0.4 per hour |
| Human Population | ~1.1% per year |
| Isotope | Decay Constant (λ) |
|---|---|
| Carbon-14 | λ = 0.000121 per year |
| Iodine-131 | λ = 0.086 per day |
| Cesium-137 | λ = 0.0023 per day |
Expert Tips
- Remember, exponential functions grow (or decay) rapidly as time increases.
- Always use a calculator for large or complex values to avoid rounding errors.
- Understand the difference between exponential growth and compound interest.
Interactive FAQ
What is the difference between exponential and linear growth?
Exponential growth increases at an accelerating rate, while linear growth increases at a constant rate.
Why is the base (e) used in exponential functions?
The base (e) is used because it is the only number that, when raised to the power of 1, equals itself.
BLS – Exponential Growth and Decay