Solution to the exponential decay equation

The solution to the exponential decay equation is the product of the initial quantity and 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:

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