Question 1008144
( 3, 192 )
( 0, 3 )
{{{ y = 3*e^(k*x) }}}
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When {{{ x=0 }}}, {{{ y = 3 }}}
{{{ y = 3*e^0 }}}
{{{ y =3 }}}
That gives me the point ( 0,3 )
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( 3, 192 )
{{{ 192 = 3*e^( k*3 ) }}}
{{{ e^( k*3 ) = 64 }}}
Take the natural log of both sides
{{{ k*3 = ln( 64 ) }}}
{{{ k = 4.1589 / 3 }}}
{{{ k = 1.3863 }}}
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The equation is:
{{{ y = 3*e^( 1.386x ) }}}
Here's the plot:
 {{{ graph( 400, 400, -1, 5, -10, 250, 3*e^( 1.386x ) ) }}}
Looks about right -hope I got it!