The growth in the population of worms, WWW, is modelled by the equation: W=120−90ektW = 120 - 90e^{kt}W=120−90ekt where k k\,k is a constant and t t\,t is the the number of days since the first measurement.
After 40 days there were 48 worms. Use this information to find a complete equation for the model, giving your value of k k\,k to 3 significant figures, and use the model to find the number of worms when measurements began and to predict the number of worms after one year.
Sketch the graph of W W\,W against ttt.
277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data. Each one has a worked solution and a mark scheme showing where the marks go.