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 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) $y = 2 e ^ { 4 x - 24 }$

Question

Quizplus · Accepted Answer

The differential equation for the curve is $\frac{dy}{dx} = 4y$. Solving this gives $y = Ce^{4x}$. Using the point $(6,2)$, we find $C = 2e^{-24}$, so the equation is $y = 2e^{4x-24}$.

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

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