Question from http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=29&t=8315&start=780

The mass of particles of a certain radioactive chemical element is halved every 10 months. During a chemical experiment, the initial mass of particles of the chemical element is 3mg.

(i) write down an expression, in terms of t, for the mass of particles after t years.

(ii) Hence, find the value of t, if the mass is reduced to 0.046875 mg after t years.

Solution:

(i)

Therefore, .

How many 10 months are there in ? (Ans: )

Hence, the mass of particles after years is mg.

(ii)

We need to solve .

Dividing by 3, we have .

Ln both sides, we have .

Hence, .

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