Question 959561
After {{{ n }}} years, the car is worth
{{{ 25000*( 1 - .2 )^n }}}
given:
{{{ 5000 = 25000*.8^n }}}
{{{ 1/5 = .8^n }}}
{{{ .2 = .8^n }}}
Take the log of both sidesd
{{{ n*log( .8 ) = log( .2 ) }}}
{{{ n = log( .2 ) / log( .8 ) }}}
{{{ n = -.69897 / -.0961 }}}
{{{ n = 7.273 }}}
In 7 years the car will be worth $5,000
check:
{{{ .2 = .8^n }}}
{{{ .2 = .8^7.273 }}}
{{{ .2 = .197 }}}
close enough I think