Question 1040263
For each city, plot {{{ p }}}, population on the
vertical axis and {{{ n ]]], number of years relative
to year 2000, on the horizontal axis
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Rate for Charleston, SC: {{{ 800 }}} p / n
Rate for Greenville, SC: {{{ -228 }}} p / n
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Equation for Charleston, SC:
{{{ p = 116300 + 800n }}}
Equation for Greenville, SC:
{{{ p = 56002 - 228n }}}
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Set the 2 populations equal to each other
{{{ 116300 + 800n = 56002 - 228n }}}
{{{ 1028n = 56002 - 116300 }}}
{{{ 1028n = -60298 }}}
{{{ n = -58.656 }}}
In 1941, ( 59 years before 2000 ), the cities populations
would have been the same
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check:
{{{ p = 116300 + 800*( -58.656 ) }}}
{{{ p = 116300 - 46924.8 }}}
{{{ p = 69375.2 }}}
and
{{{ p = 56002 - 228*( -58.656 ) }}}
{{{ p = 56002 + 13373.568 }}}
{{{ p = 69375.568 }}}
I think that's close enough
Here's the plots:
( year 2000 is at {{{ n = 0 }}} )
{{{ graph( 800, 400, -100, 20, -20000, 200000, 116300 + 800x, 56002 - 228x ) }}}