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 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, 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.