The half-life of plutonium is 9 hours. If 60 milligrams is present now, how much will be present in 2 days?

Question

The final answer is stated to be rounded one decimal place. I’m not sure of the correct way to use the formula needed.

Answer 1

Let A(t) = amount remaining after t hours

Then A(t) = A₀e^kt, where A₀ is the initial amount

A(t) = 60e^kt

Since the half-life is 9 hours, 30 = 60e^9k.

So, e^9k = 1/2.

Plugging into the formula, A(t) = 60(e^9k)^(1/9)t = 60(1/2)^1/9t

Amount remaining in 2 days (48 hours) = A(48) = 60(1/2)^48/9 = 1.49 mg