Question 338196
Approximately one-half of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. The number still in use after t years is given by the function N(t)=310,000(1/2)^t
After how many years will 5000 bottles still be in use?
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Simply set N(t) to 5000 and solve for t:
{{{ N(t)=310,000(1/2)^t }}}
{{{ 5000 = 310000(1/2)^t }}}
{{{ 5000/310000 = (1/2)^t }}}
{{{ 5/310 = (1/2)^t }}}
{{{ 1/62 = (1/2)^t }}}
{{{ log(1/2,1/62) = t }}}
applying change of base:
{{{ log(1/62)/log(1/2) = t }}}
6 years = t