Exponential Functions — Test

Question 14 • Mathematics I

Which graph is the sequence defined by the function f of x is equal to 3 times 2 raised to the x minus 1 power ?

Answer

Image with description On a coordinate plane, 5 points are plotted. The points are (0 comma 2), (1 comma 6), (2 comma 18), (3 comma 54), (4 comma 162).

Image with description On a coordinate plane, 6 points are plotted. The points are (0 comma 3), (1 comma 6), (2 comma 12), (3 comma 24), (4 comma 48), (5 comma 96).

Image with description On a coordinate plane, 5 points are plotted. The points are (1 comma 3), (2 comma 6), (3 comma 12), (4 comma 24), (5 comma 48).

Image with description On a coordinate plane, 5 points are plotted. The points are (1 comma 2), (2 comma 6), (3 comma 18), (4 comma 54), (5 comma 162).

Explanation

The function is f(x) = 3 × 2^(x − 1). Substituting x = 1 gives 3 × 2^0 = 3; each time x increases by 1, the value doubles, giving the points (1, 3), (2, 6), (3, 12), (4, 24), and (5, 48). Those are the points shown in choice C.

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