1. We start with the equation: $1.9t + 0.14 + 0.14 \sin\left(2\pi(t - 0.25)\right) = 5$ 2. Our goal is to solve for $t$. First, isolate the terms involving $t$ on one side: $1.9t + 0.14 \sin\left(2\pi(t - 0.25)\right) = 5 - 0.14$ 3. Simplify the right side: $1.9t + 0.14 \sin\left(2\pi(t - 0.25)\right) = 4.86$ 4. This is a transcendental equation because $t$ appears both linearly and inside the sine function. Such equations generally require numerical methods to solve. 5. To solve numerically, we can use an iterative method like the Newton-Raphson method or graphing to find approximate solutions. 6. For example, define the function: $$f(t) = 1.9t + 0.14 \sin\left(2\pi(t - 0.25)\right) - 4.86$$ 7. We seek $t$ such that $f(t) = 0$. 8. Using numerical approximation (e.g., graphing or a calculator), one finds that $t \approx 2.5$ satisfies the equation. 9. Therefore, the approximate solution is: $$t \approx 2.5$$ This is the value of $t$ that satisfies the original equation.