The initial phase of a biological growth process is modeled by the function B(t)=(2+κt4)7B(t) = \left( 2 + \frac{\kappa t}{4} \right)^7B(t)=(2+4κt)7, where ttt is the time in hours and κ\kappaκ is a non-zero constant.
Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of B(t)B(t)B(t). Give each term in simplest form.
Given that, in the binomial expansion of B(t)B(t)B(t), the coefficients of ttt, t2t^2t2 and t3t^3t3 are the first three terms of an arithmetic progression,
find, using algebra, the possible values of κ\kappaκ.
