7/8 part of a substance decays in 45 days what is its half life
To find the half-life of a substance, we need to know the time it takes for half of the substance to decay. In this case, we know that 7/8 of the substance decays in 45 days.
To determine the half-life, we can set up an equation:
(1/2) = (7/8)^(t/45)
Where t represents the time in days.
To solve for t, we can take the logarithm of both sides of the equation.
log((1/2)) = log((7/8)^(t/45))
Using the logarithm rule that states log(a^b) = b * log(a), we can simplify the equation:
log((1/2)) = (t/45) * log((7/8))
To isolate t, we can multiply both sides of the equation by 45:
45 * log((1/2)) = t * log((7/8))
Finally, we can divide both sides of the equation by log((7/8)) to solve for t:
t = (45 * log((1/2))) / log((7/8))
Using a calculator, we can find the numerical value for t.