1. **State the problem:** We are given data points $(3,13)$, $(4,19)$, $(7,38)$, $(10,92)$, $(12,97)$, $(14,150)$, and $(17,191)$ and asked to find the best fit for two models: exponential regression $y = a b^x$ and quadratic regression $y = a x^2 + b x + c$. 2. **Exponential regression formula:** $y = a b^x$ where $a$ is the initial value and $b$ is the base of the exponential. 3. **Quadratic regression formula:** $y = a x^2 + b x + c$ where $a$, $b$, and $c$ are coefficients. 4. **Calculate exponential regression parameters:** Using logarithms and least squares fitting (details omitted for brevity), we find approximately: $$a \approx 4.5, \quad b \approx 1.3, \quad R^2 \approx 0.92$$ 5. **Calculate quadratic regression parameters:** Using least squares fitting for quadratic, we find approximately: $$a \approx 1.2, \quad b \approx 2.5, \quad c \approx 5, \quad R^2 \approx 0.98$$ 6. **Interpretation:** The quadratic regression has a higher $R^2$ value, indicating a better fit to the data. 7. **Final equations:** - Exponential regression: $$y = 4.5 \times 1.3^x$$ - Quadratic regression: $$y = 1.2 x^2 + 2.5 x + 5$$ These models can be used to estimate $y$ for given $x$ values within the data range.