$ E(2) = 8a + 4b + 2c + d = 58 $
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- Question: A science fiction writer models the energy output $ E(t) $ of a fusion reactor on Mars as a cubic polynomial satisfying $ E(1) = 20 $, $ E(2) = 58 $, $ E(3) = 132 $, and $ E(4) = 26^3 $. Find $ E(0) $.
- Solution: Let $ E(t) = at^3 + bt^2 + ct + d $. Use the given values:
- $ E(1) = a + b + c + d = 20 $
- $ E(3) = 27a + 9b + 3c + d = 132 $
- $ E(4) = 64a + 16b + 4c + d = 26^3 = 17576 $
- Subtract (i) from (ii):
