The efficiency E E\,E of a high-pressure industrial catalyst is modeled as a function of its concentration t t\,t by the expression E(t)=(2−1.5t)9E(t) = (2 - 1.5t)^9E(t)=(2−1.5t)9.
Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of
(2−1.5t)9 (2 - 1.5t)^9 (2−1.5t)9giving each term in simplest form.
This expansion is to be used to find an approximation for the catalyst efficiency when E=1.979E = 1.97^9E=1.979. State the value of t t\,t that should be used. (There is no need to carry out this calculation.)