Answer
year $2018$
Work Step by Step
Step 1. Given the model equation $B=0.07x^2+47.4x+500$, let $B=1177$, we have $0.07x^2+47.4x+500=1177$ and $0.07x^2+47.4x-677=0$
Step 2. Solve the above equation graphically as shown in the figure, we have $x\approx14$ which means in year $2004+14=2018$
