Question

The amount A remaining of n milligrams of a radioactive isotope after t days is given by A=n(1/2)^t/10where n is the initial amount (in milligrams). Whatnercent of the isotope decays each day?

Answer 1

6.7% of the isotope decays each day

Here, we are interested in finding the the percentage of decay each day

Let us calculate the amount left after a day

From what we have, we only need to substitute the value of 1 for t

Let us have the initial amount n as 100 mg

So, we have it that;

$\begin{gathered} A_1\text{ = 100 (}\frac{1}{2})^{\frac{1}{10}} \\ A_1\text{ = 93.3033 mg} \end{gathered}$

So, to get the percentage of decay daily, we need to subtract from the amount initially which is n (which we choose as 100)

So we have;

$100\text{ - 93.3033 = 6.6967}$

In percentage, we have this as 6.7%