Exponential Growth Function
Exponential Growth Function
\[y = ae^{kx}\]
Variables
y = function value
a = initial value
k = growth constant
x = independent variable
Description
What is this formula?
This formula models exponential growth where the rate of increase is proportional to the current value. The function grows increasingly faster as x increases.
When to use it
Use this formula for systems that grow continuously at a constant percentage rate.
Example
For:
a=100
k=0.2
x=5
y=100*(℮^(0.2*5))
y=100*(℮^1)
y≈271.83
Applications
Population growth
Compound interest
Biological growth
Finance
Radioactive multiplication
Engineering modeling
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