Question

Element X is a radioactive isotope such that its mass decreases by 81% every year. If an experiment starts out with 490 grams of Element X, write a function to represent the mass of the sample after tt years, where the daily rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per day, to the nearest hundredth of a percent.

Answer 1

Answer:

We can say we start with 490 grams and after 1 year we have (490 * .81 grams) or 396.9 grams.

We can solve for half-life by this equation:

Half life = (time * log 2) / log (beginning amount / ending amount)

Half-life = (1 year * 0.30102999566) / log (490 / 396.9)

Half life = (1 year * 0.30102999566) / log (1.2345679012 )

Half life = (0.30102999566) / 0.091514981109

Half-Life = 3.2894067399  years

Well, that's a start.

Step-by-step explanation:

Answer 2

The half life of the given radioactive isotope will be 3.2894067399  years.

What is Half life period?

The amount of time it takes to disintegrate by half an initial amount. For a given reaction, a reactant's half-life t-1/2 is the time it takes for its concentration to reach a value which is the arithmetic mean of its initial and final value.

Here, Element X starts with 490 grams

After 1 year we have  (490 X 0.81 grams) or 396.9 grams

Now, We can solve for half-life by this equation:

Half life = (time  X log 2) / log (beginning amount / ending amount)

Half-life = (1 year X 0.30102999566) / log (490 / 396.9)

Half life = (1 year X 0.30102999566) / log (1.2345679012 )

Half life = (0.30102999566) / 0.091514981109

Half-Life = 3.2894067399  years

Thus, the half life of the given radioactive isotope will be 3.2894067399  years.

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