Question 314512
Use the formula N = Iekt, where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope, to the nearest year.
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Given the formula:
{{{ N = Ie^(kt) }}}
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Let x = initial amount (I)
then
N = x/2  (half-life)
k was given as -0.275% =  -0.00275
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Substitute the above and the 
{{{ N = Ie^(kt) }}}
{{{ x/2 = xe^(-0.00275t) }}}
dividing both sides by x eliminates our variable:
{{{ 1/2 = e^(-0.00275t) }}}
take ln of both sides:
{{{ ln(1/2) = -0.00275t }}}
{{{ ln(1/2)/-0.00275 = t }}}
{{{ 252.05 = t }}} years