Question

Einsteinium-253253253 is an element that loses about \dfrac23

Answer 1

Answer:

S(t) = 450 (1/3)^t .

Step-by-step explanation:

Answer 2

Answer:

                         $S(t)=450\times(1/3)^t$

Explanation:

The element is einstenium-253. That means that the mass number, i.e. numbrer of protons plus neutrons, of this isotope is 253, but that is not relevant to answer the question.

It is said that the element loses about 2/3 of its mass every month, then to find the remaining amount, every month you have to multiply by 1/3.

With that you can create a decaying function that gives a sample's mass in grams:

         

        $Initial\text{ }mass=M_0\\ \\ Mass\text{ }after\text{ }1\text{ }month=M_0\times1/3\\ \\ Mass\text{ }after\text{ }2\text{ }months=M_0\times(1/3)^2\\ \\ Mass\text{ }after\text{ }3\text{ }months=M_0\times(1/3)^3\\ \\ Mass\text{ }after\text{ }t\text{ }months=M_0\times(1/3)^t$

Now you can replace the initial mass with 450 g and write the specific function for this sample:

          $S(t)=450\times(1/3)^t$