1. **State the problem:** We are given the exponential function $$P(t) = 440 \times (1.29)^t$$ where $P(t)$ is the population size at time $t$ (in years). We need to find: - The initial population size. - Whether the function represents growth or decay. - The percent change in population size each year. 2. **Identify the initial population size:** The initial population size corresponds to $P(0)$, which is the population at time $t=0$. Using the formula: $$P(0) = 440 \times (1.29)^0$$ Since any number to the zero power is 1: $$P(0) = 440 \times 1 = 440$$ So, the initial population size is 440. 3. **Determine growth or decay:** The base of the exponential function is 1.29. - If the base is greater than 1, the function represents exponential growth. - If the base is between 0 and 1, it represents exponential decay. Since $1.29 > 1$, the function represents **growth**. 4. **Calculate the percent change each year:** The population changes by a factor of 1.29 each year. The percent change is given by: $$\text{Percent change} = (1.29 - 1) \times 100 = 0.29 \times 100 = 29\%$$ **Final answers:** - Initial population size: 440 - The function represents growth. - The population size increases by 29% each year.