Solution to the exponential decay equation

The solution to the exponential decay equation is the product of the initial quantity and the the ratio of the current time to the half-life of the quantity, raised to the power of 2. In other words, for every half-life that passes, the quantity decays by a factor of 2.

Links:

1. Wikipedia.

final_quantity

Quantity that still remains and has not decayed after time \(t\).

Symbol:

X

Latex:

\(X\)

Dimension:

any_dimension

initial_quantity

Initial quantity that will decay.

Symbol:

X_0

Latex:

\(X_{0}\)

Dimension:

any_dimension

half_life

half_life of the decaying quantity.

Symbol:

t_1/2

Latex:

\(t_{1/2}\)

Dimension:

time

time

time.

Symbol:

t

Latex:

\(t\)

Dimension:

time

law

X = X_0 * 2^(-t / t_1/2)

Latex:

\[X = X_{0} \cdot 2^{- \frac{t}{t_{1/2}}}\]