The exponential function g is defined by g x = 19 · a x , where a is a positive

Question

The exponential function g is defined by g x = 19 &#183; a x , where a is a positive constant. If g 3 = 2,375 , what is the value of g 4 ?

Accepted Answer

The correct answer is 11,875 . It's given that the exponential function g is defined by g x = 19 /mo> 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 /mo> a 3 . Dividing each side of this equation by 19 yields 125 = a 3 . 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 /mo> a x yields g 4 = 19 /mo> 5 4 , or g 4 = 11 , 875 . Therefore, the value of g 4 is 11,875 .

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