1. **State the problem:** We have a population model for coyotes given by $$P = 1024(1.078)^n$$ where $n$ is the number of years since 2005. 2. **Find the initial population in 2005:** This corresponds to $n=0$. $$P = 1024(1.078)^0 = 1024 \times 1 = 1024$$ So, the initial population was 1024 coyotes. 3. **Determine the growth rate:** The growth factor is 1.078, which means the population grows by 7.8% each year. 4. **Calculate the population in 2020:** Since 2020 is 15 years after 2005, $n=15$. $$P = 1024(1.078)^{15}$$ Calculate the power: $$1.078^{15} \approx 3.172$$ Then: $$P \approx 1024 \times 3.172 = 3247.33$$ Rounding to the nearest whole number, the population in 2020 will be approximately 3247 coyotes. **Final answers:** - Initial population in 2005: 1024 - Growth rate: 7.8% per year - Population in 2020: 3247 coyotes