\[y = ae^{-kx}\]
Variables
yfunction value
ainitial value
kdecay constant
xindependent variable
Description
What is this formula?
This formula models exponential decay where the quantity decreases proportionally to its current value. The function decreases rapidly at first and then gradually approaches zero.
When to use it
Use this formula for processes involving continuous decay or reduction at a constant percentage rate.
Example
For:
a=500
k=0.3
x=4
y=500*(℮^(-0.3*4))
y=500*(℮^(-1.2))
y≈150.60
Applications
Radioactive decay
Battery discharge
Population decline
Thermal cooling
Signal attenuation
Chemical concentration reduction