1. **State the problem:** We need to predict the population of a city after 50 years given the current population and an annual decrease rate. 2. **Given data:** - Initial population $P_0 = 954000$ - Annual decrease rate $r = 0.1\% = 0.001$ - Time $t = 50$ years 3. **Formula for exponential decay:** $$P(t) = P_0 (1 - r)^t$$ This formula is used because the population decreases by a fixed percentage each year. 4. **Substitute the values:** $$P(50) = 954000 \times (1 - 0.001)^{50} = 954000 \times (0.999)^{50}$$ 5. **Calculate the decay factor:** $$ (0.999)^{50} = e^{50 \ln(0.999)} $$ Using approximation: $$ \ln(0.999) \approx -0.0010005 $$ So, $$ e^{50 \times (-0.0010005)} = e^{-0.050025} \approx 0.9512 $$ 6. **Calculate the population after 50 years:** $$ P(50) = 954000 \times 0.9512 = 907,450.8 $$ 7. **Final answer:** The predicted population after 50 years is approximately **907,450**. This matches option D.