Exponential Decay Formula: Calculate Final Amount with Half-Life and Time Elapsed

A(t)=P(1/2)^t/h

half-life of a radioactive substance

This formula represents exponential decay, where A(t) is the final amount, P is the initial amount, t is the time elapsed, and h is the half-life of the substance or quantity being studied.

The half-life is the time it takes for half of the original amount to decay or decay in half. For example, if a substance has a half-life of 10 years, then after 10 years, half of the original amount will have decayed, and after 20 years, only one-quarter of the original amount will remain.

To use this formula, we need to determine the initial amount P, the half-life h, and the time t that has elapsed. Once we have these values, we can plug them into the formula to find the final amount A(t).

For example, let’s say we have an initial amount of 100 grams of a substance with a half-life of 5 hours. After 10 hours, we want to find out how much of the substance remains.

Using the formula A(t) = P(1/2)^(t/h), we can plug in the values and solve for A(10).

A(10) = 100(1/2)^(10/5)
A(10) = 100(1/2)^2
A(10) = 100(1/4)
A(10) = 25

Therefore, after 10 hours, only 25 grams of the substance remain.

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