The half-life of a substance is 12.. At time = 0, this substance has size 60. Calculate the size of the substance at time = 33.

Crop Image

×

Crop

The half-life of a substance is 12.

At time = 0, this substance has size 60

Calculate the size of the substance at time = 33.

Step 1: Calculate Time Difference (Δ)

Δ = t_n - t

Δ = 33. - 0

Δ = 33

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

h_n = 2.75  <-- Number of times we will reduce our original size by ½

Step 3: Calculate New Substance Size (x_n)

We go through each time starting at t = 0 all the way to h_n = 2.75

Substance size at time = 1

x₁ = ½(x₀)

x₁ = ½(60)

x₁ = 30

Substance size at time = 2

x₂ = ½(x₁)

x₂ = ½(30)

x₂ = 15

Shortcut Solution to Above

x_n = ½^h_nx₀

x_n = ½^2.75(60)