Question 1124887
Since 2000:
(a)
{{{ 190 = 244*( 1 - r )^3 }}}
{{{ .7787 = ( 1 - r )^3 }}}
Take the log of both sides
{{{ -.1086= 3*log( 1 - r ) }}}
{{{ log( 1 - r ) = -.0362 }}}
{{{ 1 - r = .92 }}}
{{{ r = .08 }}}
———————
The equation for Arturo’s house is:
{{{ V(t) = 244*( 1 - .08 )^t }}}
———————————————
(b)
{{{  158 = 124*r^3 }}}
{{{ 1.274 = r^3 }}}
Take the log of both sides
{{{ .10524 = 3* log(r) }}}
{{{ log(r) = .03508 }}}
{{{ r = 1.084 }}}
—————-
The equation for Zack’s house is:
{{{ V(t) = 124*1.084^t }}}
————————————-
(c)
Set equations equal
{{{ 244*.92^t = 124*1.084^t }}}
{{{ 1.9677 = ( 1.084/.92 )^t }}}
{{{ 1.9677 = 1.1783^t }}}
Take log of both sides
{{{ .29396 = t* .07126 }}}
{{{ t = 4.125 }}}
After 4 yrs
————————————-
Check:
Arturo:
{{{ 190 = 244*.92^3 }}}
{{{ .7787 = .7787 }}}
Zack:
{{{ 158 = 124*1.084^3 }}}
{{{ 1.2742 = 1.084^3 }}}
{{{ 1.2742 = 1.2738 }}}
Close- error may be rounding off or
my calculating. I think method is OK