1. **State the problem:** We have data points of specific gravity $x$ and percentage yield $y$ of petroleum gas. We want to estimate $y$ when $x=50$. 2. **Method:** Use linear interpolation or regression to estimate $y$ at $x=50$. Since $50$ is outside the given $x$ range, we use linear extrapolation based on the last two points. 3. **Given data points:** $$ (45.5, 20.0), (46.0, 23.7) $$ 4. **Calculate slope $m$ of the line between these points:** $$ m = \frac{23.7 - 20.0}{46.0 - 45.5} = \frac{3.7}{0.5} = 7.4 $$ 5. **Equation of the line:** $$ y - y_1 = m(x - x_1) $$ Using point $(45.5, 20.0)$: $$ y - 20.0 = 7.4(x - 45.5) $$ 6. **Estimate $y$ at $x=50$:** $$ y = 20.0 + 7.4(50 - 45.5) = 20.0 + 7.4 \times 4.5 = 20.0 + 33.3 = 53.3 $$ 7. **Interpretation:** The estimated percentage yield of petroleum gas at $x=50$ is approximately $53.3$. This is an extrapolation and may be less accurate than interpolation.