High School Exponential Growth & Decay Model Calculator
Calculate A(t) = a(1 ± r)t and visualize the trend over time.
Final Amount A(t)
Function Equation
Step-by-Step
Growth/Decay Chart
Understanding the Exponential Growth & Decay Model Calculator
Exponential models describe real-world situations where a quantity increases or decreases by a fixed percentage over equal time intervals. Unlike linear models, which add the same amount each time, exponential models multiply by a factor. This leads to curves that can rise very rapidly (growth) or flatten out toward zero (decay).
The General Formula
For high school mathematics, the standard formula used is:
- A(t): The final amount after time t.
- a: The initial amount (sometimes called P for Principal).
- r: The rate of growth or decay (expressed as a decimal).
- t: The time period.
Growth vs. Decay
Using our Exponential Growth & Decay Model Calculator, you can instantly see the difference between the two behaviors:
Growth: Occurs when the base factor (1 + r) is greater than 1. This models populations of bacteria, compound interest in bank accounts, or viral spread. The curve starts flat and shoots upward.
Decay: Occurs when the base factor (1 – r) is between 0 and 1. This models radioactive decay (half-life), depreciation of a car’s value, or cooling of coffee. The curve starts high and drops rapidly, then slows down as it approaches zero.
Real World Examples
If you buy a car for $20,000 and it depreciates at 15% per year, that is exponential decay. If you invest $1,000 at 7% annual interest, that is exponential growth.
FAQ
Yes, this is a free educational tool accessible to all students.
In the formula, percentages must be converted. 5% becomes 0.05. Our tool handles this conversion for you automatically if you enter “5”.
For decay models of this form, the asymptote is usually y=0, meaning the amount gets closer and closer to zero but never fully disappears mathematically.
Yes. A negative time value calculates what the amount was before the start time (t=0).