1. Problem: Estimate the production for the years 1964 and 1966 using the given data. Given data: Year: 1961, 1962, 1963, 1964, 1965, 1966, 1967 Production: 200, 220, 260, -, 350, -, 430 2. Formula and approach: We will use linear interpolation to estimate missing values. Linear interpolation formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ for a value $x$ is: $$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$$ 3. Estimating production for 1964: Use points (1963, 260) and (1965, 350): $$y_{1964} = 260 + \frac{(1964 - 1963)(350 - 260)}{1965 - 1963} = 260 + \frac{1 \times 90}{2} = 260 + 45 = 305$$ 4. Estimating production for 1966: Use points (1965, 350) and (1967, 430): $$y_{1966} = 350 + \frac{(1966 - 1965)(430 - 350)}{1967 - 1965} = 350 + \frac{1 \times 80}{2} = 350 + 40 = 390$$ --- 5. Problem: Find the missing term in the sequence where $x = 1,2,3,4,5,6,7$ and $y = 2,4,8,-,32,64,128$. 6. Observing the pattern: The $y$ values appear to be powers of 2: $$y = 2^x$$ 7. Calculate the missing term at $x=4$: $$y_4 = 2^4 = 16$$ Final answers: - Production in 1964 is $305$. - Production in 1966 is $390$. - Missing term in the sequence at $x=4$ is $16$.