Find the Arc Length Function for the Curve $y=10 x^{3 / 2}$

Multiple Choice

Find the arc length function for the curve $y=10 x^{3 / 2}$ with starting point $P_{0}(1,15)$ .

A) $L=\frac{2}{675}\left((1+225 x) ^{3 / 2}+226\right)$
B) $L=\frac{2}{225}\left((1+220 x) ^{3 / 2}-226 \sqrt{226}\right)$
C) $L=\frac{2}{675}\left((1+225 x) ^{5 / 2}+226 \sqrt{226}\right)$
D) $L=\frac{2}{675}\left((1+225 x) ^{3 / 2}-226 \sqrt{226}\right)$
E) $L=\frac{2}{675}\left((1+225 x) ^{1 / 2}-226 \sqrt{226}\right)$