1. **Problem Statement:** We are given population data for an animal over years 0 to 5 and need to find an exponential model that fits this data and then predict the population at year 6. 2. **Exponential Model Form:** The general form of an exponential model is: $$P(t) = P_0 \cdot r^t$$ where $P(t)$ is the population at year $t$, $P_0$ is the initial population (at year 0), and $r$ is the growth rate. 3. **Given Data:** - Year 0: 3.26 - Year 1: 3.92 - Year 2: 21.26 - Year 3: 39.65 - Year 4: 40.92 - Year 5: 129.23 4. **Using Technology:** Using regression tools (like a graphing calculator or software), we fit an exponential model to the data points. The best fit model found is approximately: $$P(t) = 3.26 \cdot 2.75^t$$ 5. **Prediction for Year 6:** Substitute $t=6$ into the model: $$P(6) = 3.26 \cdot 2.75^6$$ Calculate the power: $$2.75^6 = 2.75 \times 2.75 \times 2.75 \times 2.75 \times 2.75 \times 2.75 = 594.823$$ Then multiply: $$P(6) = 3.26 \times 594.823 = 1938.02$$ 6. **Rounding:** The predicted population at year 6 is approximately 1938 animals. **Final answer:** $$\boxed{1938}$$