Help Please, I don't understand how to start this problem

Question

The half-life of a radioactive substance is 11 days. After 20 days a sample of the substance has been reduced to a mass of 5 mg.

What was the initial mass (in mg) of the sample?

Using your answer from above, after how many days will there only be 0.5 mg of substance left?

Answer 1

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Answer 2

Hi Erika,

to solve half life problems, you use the equations:

f(t) = T₀ (1/2)^(t/t_1/2). where T₀ is initial mass and T_1/2 is the half life.

So we get f(20)= 5 = T₀•(1/2) ^ 20/11

T₀ = 17.63 mg

For the second part of the question, we plug 0.5 mg into the equation:

0.5 = 17.63 • (1/2)^ t/11

t = 56.5 days

Let me know if anything doesn't make sense!