1. The problem is to evaluate the function $$\tau(30) = 0.9 - e^{-0.2 \times 30}$$ and understand its behavior. 2. The formula involves an exponential decay term $$e^{-kt}$$ where $$k=0.2$$ and $$t=30$$. 3. Calculate the exponent first: $$-0.2 \times 30 = -6$$ 4. Evaluate the exponential term: $$e^{-6}$$ 5. Substitute back into the function: $$\tau(30) = 0.9 - e^{-6}$$ 6. Since $$e^{-6}$$ is a very small positive number (approximately 0.00247875), the function value is: $$\tau(30) \approx 0.9 - 0.00247875 = 0.89752125$$ 7. This shows the function approaches 0.9 as $$t$$ increases, due to the exponential decay term tending to zero. Final answer: $$\boxed{\tau(30) \approx 0.8975}$$