Final answer:
Samuel likely attempted to enter a number in scientific notation but included accidental keystrokes. Ignoring the initial 'G', the 'E90' part signifies an exponent of 90 in scientific notation, which suggests a large number. From the given choices, 2.5E14 seems to be the most likely display, assuming the initial 'G' was a mistake.
Step-by-step explanation:
Samuel entered the keystrokes GEO90E on his calculator. Based on the keys entered, we can interpret this as "GOE90" which looks like an attempt to enter a number in scientific notation. Since calculators generally use 'E' or 'EXP' to denote 'times 10 to the power of', we can assume that 'GEO' was an input error for 'GOE', with 'GO' possibly being an accidental prefix. Correct scientific notation input should have the form (coefficient)E(exponent), like '2.5E14'.
Without having the exact model of the calculator, it's hard to determine the exact output. However, if we ignore the incorrect prefix 'GO', the input 'E90' should lead the calculator to attempt to display a number in scientific notation with an exponent of 90. This would result in a very large number; however, without the coefficient it is incomplete. Among the choices given and assuming the 'G' keystroke was a mistake, the most reasonable result based on only the correct part of his input ('E90') would arguably be 2.5E14, as the choices with negative exponents are implausible with such a high positive exponent and the choice with positive exponent 5 is too low.