Question

A radioactive element decays exponentially at a rate of 0.13% each hour. Which of the following is true?

There will be slightly more radioactive element in 24 hours.
The amount of radioactive element will continue to grow infinitely large.
If there are 1,000 grams of the element, there will be 756.9 grams in two hours.
The amount of the element will decrease closer and closer to zero as time goes on.

Answer 1

The last sentence is the correct one.

Answer 2

(d) The amount of the element will decrease closer and closer to zero as time goes on.

Explanation:

Since radioactive element is decay exponentially. So, its value will decreases continuously.

Thus, Options (a) and (b) are wrong.

And Option (d) is correct. Since amount of element will decrease continuously and it will get closer to zero.

For calculating the amount in two hours, we use formula:

`\text{Final Amount} = (\text{Initial Amount})* e^(-0.13*2)`

\Rightarrow \text{Final Amount} = 1000\times e^{-0.13\times2} = 771.05[/tex]

Thus, Option (c) is also incorrect option.