The growth of a population of insects in a laboratory is being monitored. The total number of insects, NNN, at time ttt weeks after the start of the study is modelled by the equation
log10N=2.15+0.26t\log_{10} N = 2.15 + 0.26tlog10N=2.15+0.26t
Write this equation in the form N=abtN = ab^tN=abt, where aaa and bbb are constants to be found. Give each value to 4 significant figures.
When t=Tt = Tt=T, the population of insects is 8000. Find the value of TTT according to the model, giving your answer to 3 significant figures.
The laboratory space can accommodate a maximum of 25,000 insects. Determine whether or not the population will exceed this limit within the first 8 weeks of the study.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, 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.