1. **Problem statement:** Predict the population of a city in 50 years given the current population is 954,000 and it is decreasing at an annual rate of 0.1%. 2. **Formula used:** The population after $t$ years with a decay rate $r$ is given by the exponential decay formula: $$ P(t) = P_0 (1 - r)^t $$ where: - $P_0 = 954000$ (initial population), - $r = 0.001$ (0.1% expressed as a decimal), - $t = 50$ years. 3. **Calculate the population after 50 years:** $$ P(50) = 954000 \times (1 - 0.001)^{50} = 954000 \times (0.999)^{50} $$ 4. **Evaluate the power:** $$ (0.999)^{50} \approx 0.9512 $$ 5. **Multiply to find the population:** $$ P(50) = 954000 \times 0.9512 = 907,450.8 $$ 6. **Interpretation:** The population after 50 years is approximately 907,450. **Final answer:** The predicted population in 50 years is about **907,450**.