1. **State the problem:** We want to find the best fit line for the data points (50, 64.7), (60, 51.3), (70, 40.5), (90, 25.9), (100, 7.5) using the least squares method for the model $Y = X^A \cdot B$. 2. **Transform the model:** Taking natural logarithms on both sides gives: $$\ln Y = A \ln X + \ln B$$ Let $y = \ln Y$, $x = \ln X$, and $c = \ln B$. The model becomes linear: $$y = A x + c$$ 3. **Calculate $x$ and $y$ values:** \begin{align*} &x_i = \ln X_i, \quad y_i = \ln Y_i\\ &(50, 64.7) \to (\ln 50, \ln 64.7) \\ &(60, 51.3) \to (\ln 60, \ln 51.3) \\ &(70, 40.5) \to (\ln 70, \ln 40.5) \\ &(90, 25.9) \to (\ln 90, \ln 25.9) \\ &(100, 7.5) \to (\ln 100, \ln 7.5) \end{align*} 4. **Compute sums needed for least squares:** Calculate $\sum x_i$, $\sum y_i$, $\sum x_i y_i$, $\sum x_i^2$, and $n=5$. 5. **Formulas for slope $A$ and intercept $c$:** $$A = \frac{n \sum x_i y_i - \sum x_i \sum y_i}{n \sum x_i^2 - (\sum x_i)^2}$$ $$c = \frac{\sum y_i - A \sum x_i}{n}$$ 6. **Calculate $A$ and $c$ using the sums from step 4.** 7. **Find $B$ by exponentiating $c$:** $$B = e^c$$ 8. **Write the final fitted model:** $$Y = B X^A$$ This model best fits the data in the least squares sense.