Initial Size of at time =
<-- Half-Life
<-- Evaluate at time tn
  

The half-life of a substance is 1

At time = 0, this substance has size 100

Calculate the size of the substance at time = 7

Step 1: Calculate Time Difference (Δ)

Δ = tn - t

Δ = 7 - 0

Δ = 7

Step 2: Calculate number of half-lives (hn)

hn  =  Δ
  h

hn  =  7
  1

hn = 7  <-- Number of times we will reduce our original size by ½

Step 3: Calculate New Substance Size (xn)

We go through each time starting at t = 0 all the way to hn = 7

Substance size at time = 1

x1 = ½(x0)

x1 = ½(100)

x1 = 50

Substance size at time = 2

x2 = ½(x1)

x2 = ½(50)

x2 = 25

Substance size at time = 3

x3 = ½(x2)

x3 = ½(25)

x3 = 12.5

Substance size at time = 4

x4 = ½(x3)

x4 = ½(12.5)

x4 = 6.25

Substance size at time = 5

x5 = ½(x4)

x5 = ½(6.25)

x5 = 3.125

Substance size at time = 6

x6 = ½(x5)

x6 = ½(3.125)

x6 = 1.5625

Substance size at time = 7

x7 = ½(x6)

x7 = ½(1.5625)

x7 = 0.78125

Shortcut Solution to Above

xn = ½hnx0

xn = ½7(100)

xn  =  100
  128

xn = 0.78125


You have 2 free calculationss remaining




What is the Answer?
xn = 0.78125
How does the Half-Life of a Substance Calculator work?
Free Half-Life of a Substance Calculator - Given a half-life (h) of a substance at time t, this determines the new substance size at time tn, otherwise known as decay.
This calculator has 4 inputs.

What 4 formulas are used for the Half-Life of a Substance Calculator?

Δ = tn - t
Number of half lives = Δ/half life
Half Life Remaining = 1/2 * Prior Amount


For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Half-Life of a Substance Calculator?

decay
Reduction in size from decomposition
exponent
The power to raise a number
half-life
time required for a quantity to reduce to half its initial value
substance
Example calculations for the Half-Life of a Substance Calculator

Half-Life of a Substance Calculator Video


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