The radioactive element polonium decays according to the law

The radioactive element polonium decays according to the law given below where Q₀ is the initial amount and the time t is measured in days.

Q(t) = Q₀ · 2^-(t/140)

If the amount of polonium left after 700 days is 35 mg, what was the initial amount present?
mg

Solution

Solution

the amount of polonium left after 700 days is 35 mg

therefore

using given expression

Q(t) = Q_o · 2^(-t/140)

Plug t = 700 and Q(t) = 35

35 = Q_o (2)^-(7oo/140)

35 = Q_o (2)^-5

Q_o = 35 * 32 = 1120 gm