The rate of growth of a specific bacteria population in a petri dish, G(t)G(t)G(t) in thousands of bacteria per hour, is modeled by the function
G(t)=122+2t+4 G(t) = \frac{12}{2 + \sqrt{2t + 4}} G(t)=2+2t+412for 0≤t≤160 \le t \le 160≤t≤16, where t t\,t is the time in hours since the start of the experiment. Using the substitution u=2+2t+4u = 2 + \sqrt{2t + 4}u=2+2t+4, find the exact total increase in the population over the 16-hour period by calculating the value of
∫016122+2t+4 dt \int_{0}^{16} \frac{12}{2 + \sqrt{2t + 4}} \, dt ∫0162+2t+412dtGive your answer in the form a+blnca + b \ln ca+blnc, where a,b, a, b,\,a,b, and c c\,c are integers.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, 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.
