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 560 days is 15 mg, what was the initial amount present?

Solution

Q(t)=Q₀2^(-t/140)

t=560 days

Q(t)=15 mg

15=Q₀(2)^-560/140

15=Q₀(2)^-4

15=Q₀(1/16)

Q₀=15*16=240mg

SO the initial amount is 240 mg