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 + 0.26t log10N=2.15+0.26tWrite 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.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.