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 (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.