A quantitative analyst models the projected value of a high-risk portfolio using the function V(x)=(4+kx)7V(x) = (4 + kx)^7V(x)=(4+kx)7, where xxx represents market volatility and kkk is a positive sensitivity constant.
Find the first three terms, in ascending powers of xxx, in the expansion of
(4+kx)7 (4 + kx)^7 (4+kx)7giving each term in its simplest form.
Given that the coefficient of x2x^2x2 is exactly three-eighths of the coefficient of xxx, determine the value of kkk.
