\[y = ae^{kx}\]
Variables
yfunction value
ainitial value
kgrowth constant
xindependent 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