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Answer :
Final answer:
It will take approximately 246 minutes for the element to decay to 80 grams.
Explanation:
To determine how long it will take for the element to decay to 80 grams, we can set up a decay equation using the given information. We have an initial mass of 990 grams and a decay rate of 16.9% per minute. Let's denote the time it takes for the mass to decay to 80 grams as t.
Using the formula for exponential decay, we can write the equation as:
[tex]990 * (1 - 0.169)^t = 80[/tex]
Simplifying the equation:
[tex](0.831)^t = 80/990[/tex]
Taking the natural logarithm of both sides
t * ln(0.831) = ln(80/990)
Dividing both sides by ln(0.831):
t = ln(80/990) / ln(0.831)
Using a calculator, we find t to be approximately 246 minutes.
Therefore, it will take approximately 246 minutes for the element to decay to 80 grams.
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