Half-Life Question Percentage needed

Question

A) The half-life of radium-226 is 1620 years. If the initial quantity of radium is Q₀, write a formula for the quantity, Q, of radium left after t years.

Answer I got: Q₀(1/2)^t/1620

B) What percentage of the original amount of radium is left after 310 years? (Round to one decimal place)

I cant seem to get the percentage. Could someone please help?

Answer 1

The function is Q(t) = Q₀(1/2)^t/1620 where Q(t) is the amount of material at any time "t". That means Q(t)/Q₀ would be the percentage of the original amount at any time "t". Perhaps it would be easier to allow Q₀ to equal 100 and then, for instance, if the amount of material left is 25, then that would be 25% of the original amount.

So:

Q(t) = Q₀(1/2)^t/1620

Q(310) = Q₀(1/2)^310/1620

Q(310)/Q₀ = (1/2)^0.191358 = 0.87578 or the percentage of material is 87.578%