A Curve Passes Through the Point $( 6,2 )$ And Has the Property That the Slope of the Curve

Multiple Choice

A curve passes through the point $( 6,2 )$ and has the property that the slope of the curve at every point $P$ is 4 times the $\mathrm { y }$ -coordinate $P$ . What is the equation of the curve?

A) $y = 2 e ^ { 4 x - 6 }$
B) $y = 2 e ^ { x - 24 }$
C) $y = 2 e ^ { 4 x + 24 }$
D) $y = \frac { e ^ { 4 x - 24 } } { 2 }$
E) $y = 2 e ^ { 4 x - 24 }$