The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 3 mg. What was the initial mass of the sample? What mg is left 6 days from the start?

Answer 1

When a quantity increases or decreases by multiplication or division, it can be modeled by an exponential function like this problem where the quantity is halved every 4 days. Specifically, half-life models are:

A = A₀(1/2)^(t/λ)

where

A is the amount of substance

A₀ is the initial amount of substance

t is the time elapsed

λ is the half-life

If Palladium has a half-life of of 4 days then the model is

A = A₀(1/2)^(t/4)

We are given that A = 3 mg when t = 24 days. We substitute these values into our palladium model and then solve for A₀

3 = A₀ (1/2)^(24/4)

3 = A₀ (1/2)⁶

3 = A₀ (0.015625)

A₀ = 192

Thus, the initial mass of the sample is 192 mg and the model is

A = 192(1/2)^(t/4)

Simply plug t = 6 days into this complete model to finish the problem