1. **State the problem:** Find the arc length of the function $f(x) = 0.6x^{0.51} + 3$ over a given interval $[a,b]$. 2. **Formula for arc length:** The arc length $L$ of a curve $y=f(x)$ from $x=a$ to $x=b$ is given by: $$L = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$$ 3. **Find the derivative:** $$\frac{dy}{dx} = 0.6 \times 0.51 x^{0.51 - 1} = 0.306 x^{-0.49}$$ 4. **Square the derivative:** $$\left(\frac{dy}{dx}\right)^2 = (0.306)^2 x^{-0.98} = 0.093636 x^{-0.98}$$ 5. **Set up the integral:** $$L = \int_a^b \sqrt{1 + 0.093636 x^{-0.98}} \, dx$$ 6. **Interpretation:** To find the exact arc length, evaluate this integral over the desired interval $[a,b]$. This integral may require numerical methods for evaluation. **Note:** Without specific interval limits, the arc length formula is expressed as above.