1. **Problem 7a:** Find the energy produced by wind turbines in 1992. Given the model: $$E = 6.49(1.058)^t$$ where $t$ is years since 1980. Since 1992 is $1992 - 1980 = 12$ years after 1980, substitute $t=12$: $$E = 6.49(1.058)^{12}$$ Calculate the power: $$1.058^{12} \approx 2.012$$ So, $$E = 6.49 \times 2.012 = 13.06$$ gigawatt-hours (rounded to two decimals). 2. **Problem 7b:** Find the energy produced by wind turbines in the current year (assume 2024). Calculate $t = 2024 - 1980 = 44$. Substitute $t=44$: $$E = 6.49(1.058)^{44}$$ Calculate the power: $$1.058^{44} \approx 12.03$$ So, $$E = 6.49 \times 12.03 = 78.07$$ gigawatt-hours (rounded). 3. **Problem 8a:** Write an exponential growth equation for population. Given initial population $P_0 = 2500$ at $t=0$ and population $P = 43000$ at $t=8$. General form: $$P = P_0 r^t$$ Find growth rate $r$: $$43000 = 2500 r^8$$ Divide both sides by 2500: $$\frac{43000}{2500} = r^8$$ $$17.2 = r^8$$ Take the 8th root: $$r = \sqrt[8]{17.2}$$ Calculate: $$r \approx 1.435$$ So the equation is: $$P = 2500 (1.435)^t$$ 4. **Problem 8b:** Find population after 3 days. Substitute $t=3$: $$P = 2500 (1.435)^3$$ Calculate power: $$1.435^3 \approx 2.954$$ So, $$P = 2500 \times 2.954 = 7385$$ (rounded to nearest whole number). **Final answers:** 7a) $13.06$ gigawatt-hours 7b) $78.07$ gigawatt-hours 8a) $P = 2500 (1.435)^t$ 8b) $7385$ population after 3 days