Let's solve the problem step by step. ### Given: - Tool exponent, \( n = 0.5 \) - Constant, \( C = 100 \) - Cutting speed, \( V = 5 \) m/min ### Formula: The **Taylor's Tool Life Equation** is: \[ VT^n = C \] Where: - \( V \) = cutting speed (m/min) - \( T \) = tool life (min) - \( n \) = tool life exponent - \( C \) = constant ### Substitute the values: \[ 5 \cdot T^{0.5} = 100 \] ### Solve for T: \[ T^{0.5} = \frac{100}{5} \] \[ T^{0.5} = 20 \] Square both sides to get T: \[ T = 20^2 = 400 \] ### **Answer:** The tool life is **400 minutes**. So, the correct answer is: **400** (Option in line 8)