The population P(t)P(t)P(t), in thousands, of a species in a controlled environment is estimated using the model P(t)=15(25+At)−12\displaystyle P(t) = 15(25 + At)^{-\frac{1}{2}}P(t)=15(25+At)−21, where t t\,t is the time in years since the study began (t≥0t \ge 0t≥0). The binomial expansion of P(t)P(t)P(t) in ascending powers of t t\,t is given as B−625t+Ct2+…\displaystyle B - \frac{6}{25}t + Ct^2 + \dotsB−256t+Ct2+…
Determine the exact values of the constants AAA, BBB, and CCC.
State the range of values of t t\,t for which this expansion is valid.
For the expansion, find the coefficient of the term in t3t^3t3.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.