1. The problem asks to create a function $t(n)$ to model the growth of Lin's tetra population, where $n$ is the number of months since she bought the tetras. 2. From the table, the population values are: $$\begin{array}{c|ccccc} n & 0 & 1 & 2 & 3 & 4 \\ t(n) & 8 & 16 & 24 & 32 & 40 \\\end{array}$$ 3. We observe the population increases by 8 tetras each month, indicating a linear growth. 4. The general form of a linear function is: $$t(n) = mn + b$$ where $m$ is the rate of change (slope) and $b$ is the initial value (population at $n=0$). 5. From the data, the initial population is $t(0) = 8$, so $b = 8$. 6. The rate of change $m$ is the difference in population divided by the difference in months: $$m = \frac{t(1) - t(0)}{1 - 0} = \frac{16 - 8}{1} = 8$$ 7. Therefore, the function modeling the population is: $$t(n) = 8n + 8$$ 8. This function means every month, the population increases by 8 tetras starting from 8 at month 0. Final answer: $$\boxed{t(n) = 8n + 8}$$