(i) To find \(\frac{dx}{dt}\), we differentiate \(x = 0.7 \sqrt{(2t - 1)}\) with respect to \(t\).

Let \(u = 2t - 1\), then \(x = 0.7 u^{1/2}\).

\(\frac{dx}{du} = 0.7 \cdot \frac{1}{2} u^{-1/2} = 0.35 u^{-1/2}\).

\(\frac{du}{dt} = 2\).

By the chain rule, \(\frac{dx}{dt} = \frac{dx}{du} \cdot \frac{du}{dt} = 0.35 u^{-1/2} \cdot 2 = 0.7 (2t - 1)^{-1/2}\).

(ii) To find the rate of growth when the snake is 5 years old, substitute \(t = 5\) into \(\frac{dx}{dt}\).

\(\frac{dx}{dt} = 0.7 (2(5) - 1)^{-1/2} = 0.7 (10 - 1)^{-1/2} = 0.7 \cdot 3^{-1/2}\).

\(\frac{dx}{dt} \approx 0.23\).