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

question 60

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) \(x = \frac { 1 } { p - 1 } \left( p ^ { 2 } - 25 \right) ^ { 1 / 2 } + 699\)

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