The required equation is g(x) = 10(3)x which is the correct answer would be an option (A).
The graph of g(x) is obtained by stretching the graph of f(x) vertically by a factor of 2.
Since the vertical stretch of a graph multiplies the y-coordinates of each point on the graph by a constant factor, the equation of g(x) must be obtained by multiplying the y-coordinate of each point on the graph of f(x) by 2.
In the given equation f(x) = 5(3)x, the y-coordinate of each point on the graph of f(x) is 5(3)x.
Thus, to stretch the graph of f(x) vertically by a factor of 2, we need to multiply this y-coordinate by 2 to get the y-coordinate of the corresponding point on the graph of g(x). This gives us the following equation for g(x):
⇒ g(x) = 2 × 5(3)x = 10(3)x
Therefore, the required equation is g(x) = 10(3)x.
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