#### A PHP Error was encountered

Severity: Warning

Message: count(): Parameter must be an array or an object that implements Countable

Filename: controllers/calculator.php

Line Number: 37

Exponential Decay Calculator

# Exponential Decay Calculator

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

#### SIGN UP FOR A FREE TRIAL

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

decay.

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)