Exponential decay formula is :
Where a≠0, b≠1 , b represent growth or decay factor (or rate) and x is any real number.
But if a radioactive isotope decays in half every year which means the decay factor or decay rate is 50% or .
So, the formula for half decay will be:
Where represent c) The rate of isotope decreases.
Let assume that is a rational number. Therefore it can be expressed as a fraction
where
and
.
This means that is divisible by 7, and therefore also
is divisible by 7.
So, where
Analogically to -------
is divisible by 7 and therefore so is
.
But if both numbers and
are divisible by 7, then
which contradicts our earlier assumption that
.
Therefore is an irrational number.