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.
