how to compute this problem?
a certain element has a half life of 12 years. if there were 1000 milligrams originally, find the remaining amount after 20 years?
1000 mg*(1/2)^(20/12)
= 1000 mg*(1/2)^(5/3)
= 1000 mg*(1/2)^1.6667 = 315 mg
I used a hand calculator with a y^x key.
You can also use Google calculator.
http://www.google.com/search?q=1000*%281%2F2%29^%285%2F3%29&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
Ratios and Rates.
Questions: What is the ratio of gold protons to silver protons with gold being 79 and silver being 47?
To compute the remaining amount of a certain element after a given number of years, we can use the formula for exponential decay:
Remaining Amount = Initial Amount * (1/2)^(Time / Half-Life)
Given that the initial amount is 1000 milligrams and the half-life is 12 years, we can substitute these values into the formula:
Remaining Amount = 1000 * (1/2)^(20 / 12)
To further simplify, we can calculate the exponent first:
20 / 12 = 1.67
Now, substitute this value back into the formula:
Remaining Amount = 1000 * (1/2)^1.67
Calculating the value inside the parentheses:
(1/2)^1.67 = 0.429
Finally, compute the remaining amount:
Remaining Amount = 1000 * 0.429 = 429 milligrams
Therefore, the remaining amount of the certain element after 20 years would be 429 milligrams.