Question 1136210
All the units in the equation have to be consistent, so
the terms must look like:
[ thousands of tons ] = [ thousands of tons ] + [ thousands of tons ]
The constant term just shifts the graph up or down ( up in this case )
and has no effect on the slope
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(a)
The units of the {{{ 32t }}} are broken down like this:
[ thousands of tons ] = [ ( thousands of tons / year ) x ( years ) ]
This is [ slope ] x [ time ], so the slope is {{{ 32 }}}
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(b)
32 thousand tons / year
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The year 2005 is {{{ t = 0 }}} on the graph, so
{{{ f(t) = 200 + 32*0 }}}
{{{ f(t) = 200 }}}
200 thousand tons were mined by 2005
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Here's the graph:
{{{ graph( 400, 400, -1, 10, -100, 600, 200 + 32x ) }}}