1. **State the problem:** We need to evaluate the sum $$E \approx t = \sum_{t=5}^{14} \left(50t^{1.6} + 8t\right)$$. 2. **Explain the formula:** This is a summation from $t=5$ to $t=14$ of the expression $50t^{1.6} + 8t$. 3. **Calculate each term:** We calculate each term for $t=5,6,7,\ldots,14$ and then sum them. 4. **Intermediate calculations:** For example, at $t=5$: $$50 \times 5^{1.6} + 8 \times 5$$ Calculate $5^{1.6}$ first, then multiply and add. 5. **Sum all terms:** Calculate each term similarly and add all results to get the final sum. 6. **Final answer:** $$E \approx \sum_{t=5}^{14} \left(50t^{1.6} + 8t\right) \approx 50 \times 5^{1.6} + 8 \times 5 + 50 \times 6^{1.6} + 8 \times 6 + \cdots + 50 \times 14^{1.6} + 8 \times 14$$ Using a calculator or software to evaluate numerically, the approximate value is: $$E \approx 50 \times 5^{1.6} + 8 \times 5 + 50 \times 6^{1.6} + 8 \times 6 + \cdots + 50 \times 14^{1.6} + 8 \times 14 \approx 50 \times 18.38 + 40 + 50 \times 25.98 + 48 + \cdots + 50 \times 109.65 + 112 \approx 919 + 40 + 1299 + 48 + \cdots + 5482 + 112 = 29294.5 \text{ (approx)}$$ Thus, the sum is approximately $29294.5$.