/sci/ - Science & Math

>>5493385
>>5493523
>>5493530

Let 't' represent the elapsed time since the tree from which the charcoal came, died, and let 'x' represent the amount of <span class="math">C^{14}[/spoiler] present in the dead tree at any time 't'. Then the instantaneous rate at which the element <span class="math">C^{14}[/spoiler] decomposes is expressed in mathematical symbols as

<div class="math">\frac{dx}{dt}\cdot </div> <span class="math"> (1.1) [/spoiler]

We now make the assumption that this rate of decomposition of <span class="math">C^{14}[/spoiler] varies as the first power of 'x' (remember 'x' is the amount of <span class="math">C^{14}[/spoiler] present at any time 't'). Then the equation which expresses this assumption is

<div class="math">\frac{dx}{dt} = -kx</div> <span class="math"> (1.11) [/spoiler]

where k > 0 is a proportionality constant, and the negative sign is used to indicate that 'x', the quantity of <span class="math">C^{14}[/spoiler] present, is decreasing. Equation (1.11) is a differential equation.