Find the Supply Function $x = f ( p )$ That Satisfies

Multiple Choice

Find the supply function $x = f ( p )$ that satisfies $\frac { d x } { d p } = p \sqrt { p ^ { 2 } - 25 }$ and the initial condition x = 700 when $p = \$ 13$ .

A) $x = \frac { 1 } { 3 } \left( p ^ { 2 } - 25 \right) ^ { 3 / 2 } + 124$
B) $x = \frac { 1 } { 3 } \left( p ^ { 2 } - 25 \right) ^ { 1 / 2 } + 696$
C) $x = \frac { 1 } { 3 } ( p - 5 ) + 124$
D) $x = \frac { 1 } { 5 } \left( p ^ { 2 } - 25 \right) ^ { 3 / 2 } + 127$
E) $x = \frac { 1 } { p - 1 } \left( p ^ { 2 } - 25 \right) ^ { 1 / 2 } + 699$