A certain radioactive compound decays at a rate of 0.0345% per year. Given 200 grams of the compound, how much will remain after 500 years? After 5000 years? How about 500 years ago?

After 500 years = 165.5 grams

After 5000 years = 0 grams

500 years ago = 234.5g grams

Step-by-step explanation:

This radioactive compound decays at 0.0345% per year

For 200 grams of the compound it decays at a rate of 0.0345% per year

0.0345% of 200 = 345 / 100,000 * 200

= 0.069

So, for every year, 0.069 grams of this compound decays

In 500 years, (0.069 * 500) of this compound will decay

This gives 34. 5 grams

Therefore, Th amount which will remain after 500 years is;

200 - 34. 5 = 165.5 grams

After 5000 years,

200 - (0.069 * 5000) will remain

= 200 - (345)

= - 145

Since the value is negative, it means that all of the compound would have decayed after 5000 years so, there will be nothing left = 0 grams

The amount of the compound 500 years ago will be;

200 + (0.069 * 500)

= 200 + (34.5)

= 234.5g grams