Question

The amount, A, in milligrams, of radioactive material remaining in a container can be modeled by the exponential function A(t) = 5(0.5)0.25t, where t is time, in years. Based on this model, how many years does it take for half of the original radioactive material to be left remaining?

Answer 1

Answer: 4 years

Step-by-step explanation:

A(0) has to be amount at start. Assume that's 5mg

Then A(t) = 5×(0.5)^(0.25t) = 5×2^(-t/4),

(also known as 5 exp(-λ t) with λ = ln(2)/4, incidentally).

We need to such that A(t) = 2.5mg, or 2^(-t/4) is 1/2, which happens when -t/4 is -1, or t is 4.