OG详解-OG10 数学2 Q14

The correct answer is 11,875. It’s given that the exponential function g is defined by g(x) = 19 · a^x , where a is a positive constant, and g(3) = 2,375. It follows that when x = 3, g(x) = 2,375. Substituting 3 for x and 2,375 for g(x) in the given equation yields 2,375 = 19· a³. Dividing each side of this equation by 19 yields 125 = a³. Taking the cube root of both sides of this equation gives a = 5. Substituting 4 for x and 5 for a in the equation g(x) = 19 · a^x  yields g(4) = 19 · 5⁴ , or g(4) = 11,875. Therefore, the value of g(4) is 11,875.