1. We are given the formula for the tiger population after $t$ years: $$a = 4000 + 50 \sqrt{t}$$ 2. The problem asks to find the population after 4 years, so we substitute $t=4$ into the formula. 3. Substitute and simplify step-by-step: $$a = 4000 + 50 \sqrt{4}$$ $$a = 4000 + 50 \times 2$$ $$a = 4000 + 100$$ $$a = 4100$$ 4. This means after 4 years, there are 4100 tigers living in the wild. 5. The formula uses a square root function, which grows slower than linear functions, indicating the population increases but at a decreasing rate over time. 6. To fill the table for $t = 0,1,2,3,4,5$, calculate $a$ for each $t$ using the same formula. Final answer: After 4 years, the tiger population is $4100$.