Final answer:
The average fuel economies for passenger cars in the US in 1986, 2001, and 2015 can be calculated using the quadratic model provided, yielding approximately 12.58 mpg, 16.87 mpg, and 18.12 mpg, respectively.
Step-by-step explanation:
The question asks for the calculation of average fuel economy for passenger cars in the US at different points in time using a quadratic model. The model is given as F(t) = -0.0068t^2 + 0.47t + 10, where t is the number of years since 1980. To find the average fuel economy for the years 1986, 2001, and 2015, we substitute the corresponding values for t into the equation and solve for F(t).
- For 1986 (t = 6): F(6) = -0.0068(6)^2 + 0.47(6) + 10
- For 2001 (t = 21): F(21) = -0.0068(21)^2 + 0.47(21) + 10
- For 2015 (t = 35): F(35) = -0.0068(35)^2 + 0.47(35) + 10
We then complete the calculations:
- F(6) = -0.0068(36) + 2.82 + 10 = -0.2448 + 2.82 + 10 ≈ 12.5752 mpg
- F(21) = -0.0068(441) + 9.87 + 10 = -2.9988 + 9.87 + 10 ≈ 16.8712 mpg
- F(35) = -0.0068(1225) + 16.45 + 10 = -8.33 + 16.45 + 10 ≈ 18.12 mpg
Therefore, the average fuel economies for the years 1986, 2001, and 2015 are approximately 12.58 mpg, 16.87 mpg, and 18.12 mpg, respectively.