1. **State the problem:** Write the function \(f(t) = \begin{cases}1 - t, & 0 < t < 1 \\ 0, & t \geq 1 \end{cases}\) in terms of the unit step function \(u(t)\). 2. **Recall the unit step function:** \(u(t) = 0\) if \(t < 0\), and \(u(t) = 1\) if \(t \geq 0\). 3. **Express \(f(t)\) using unit step functions:** To restrict the function \(1 - t\) to the interval \(0 < t < 1\), we use \(u(t)\) and \(u(t-1)\). 4. Write \(f(t) = (1 - t)(u(t) - u(t - 1))\). This is because \(u(t)\) activates the function from \(t = 0\) onward, and \(u(t-1)\) subtracts it starting from \(t = 1\). 5. **Final answer:** $$f(t) = (1 - t) \bigl(u(t) - u(t - 1)\bigr)$$