Question 1101063
{{{ V(t) = 57000*e^(-.2t) + 3500 }}}
{{{ 5000 = 57000*e^(-.2t) + 3500 }}}
{{{ 57000*e^(-.2t) = 1500 }}}
{{{ e^(-.2t) = .0263158 }}}
Take the natural log of both sides
{{{ -.2t = -3.63759 }}}
{{{ t = 18.18793 }}}
and
{{{ .18793*12 = 2.255 }}}
It will take 18 yrs and 2 mos to
depreciate to $5,000
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check:
{{{ 57000*e^(-.2t) = 1500 }}}
{{{ 57000*e^(-3.63759) = 1500 }}}
{{{ 57000*.0263157 = 1500 }}}
{{{ 1499.9942 = 1500 }}}
close enough