Exponential decay is the rate at which a value or a quantity continuously decreases over a period of time. In
exponential decay, the initial amount is greater than the following amount as the amount keeps decreasing
with time. Exponential decay calculator is the online tool which can instantly give results to questions on
Example 1: Given an amount of a substance initially is 120. In a time period of 3days, how much
amount of the substance is left over? Rate of decay is -0.035.
Exponential decay formula > At= A0* ekt
Where At= amount present after time‘t’.
A0 =initial amount, k =rate of decay, t= time period of decay
Given, initial amount, A0 = 120
Time, t = 3 and rate of decay, k = -0.035
At = (120)* (e(-0.035*3) > At = 120 * (0.9003) > At = 108.04
Example 2: Given population in a small town is 500 people. The number of people in the town is
decreasing exponentially over a period of time. If the rate of decay is -0.02, then by how much
time will there be half of the population left?
Exponential decay formula > Pt= P0* ekt
Pt=population present after time‘t’=250
P0=initial population= 500, k =rate of decay=-0.02
t= time period of decay also called as Half-life in this case
250 = 500 * e(-0.02*t)
250/500= e(-0.02*t) > e(-0.02*t)=1/2
Apply natural logarithm ‘ln’ on both sides
ln(e(-0.02*t))=ln(1/2) > -0.02t= -0.693 > t = 35 days(approximately)