•A radioactive material A (decay constant λA) decays into a material B (decay constant λB) and then into material C (decay constant λC) which is also radioactive. Determine the amount of material C remaining after a time t?

 The amount of C remaining after time t is

Explanation:

We can represent the decay sequence as

The reason we added D is because we are told from the question that C is also radioactive so it has the  tendency to decay

Generally for every decay the remaining radioactive element can be obtained as

Where N is the amount of the remaining radioactive material

            is the original amount amount of the radioactive material before decay

    and   is the decay constant

Now for the decay from    amount of radioactive element B formed from A after time t can be obtained as

Where is the decay constant of A

  Now for the decay from    amount of radioactive element C formed from A after time t can be obtained as

Where is the decay constant of B

  Now for the decay from    amount of radioactive element D formed from A after time t can be obtained as

So this amount of  D is the reaming amount of the radioactive material C

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form