Final answer:
To determine how long it takes for an element to decay from 600 grams to 2 grams, we utilize the decay formula with a decay rate of 29.5% per minute. The decay time is found by solving the equation 2 = 600 * (0.705)^t, where t is the time in minutes. Calculating this and rounding to the nearest minute will give us the answer.
Step-by-step explanation:
To find out how long it will take for an element with an initial mass of 600 grams to decay until only 2 grams remain, we need to use the decay formula. The problem states that the element decays by 29.5% per minute. This implies that after each minute, 70.5% (100% - 29.5%) of the substance remains.
We can set up the equation as follows, with N being the final amount of substance (2 grams) and No being the initial amount of substance (600 grams):
N = No * (0.705)^t
Where t is the number of minutes. Plugging in the numbers we get:
2 = 600 * (0.705)^t
To solve for t, we first divide both sides by 600:
(2/600) = (0.705)^t
Then we take the natural logarithm (ln) of both sides to get rid of the exponent:
ln(2/600) = t * ln(0.705)
Now, we can solve for t:
t = ln(2/600) / ln(0.705)
After calculating the above expression, we will round t to the nearest minute to find the answer.