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?

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Mathematics

29 April, 22:18

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?

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Lucia Sullivan · 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.