The growth in the population of worms, WWW, is modelled by the equation: W=95−75ektW = 95 - 75e^{kt}W=95−75ekt where k k\,k is a constant and t t\,t is the the number of days since the first measurement.
Use the model to find the number of worms when measurements began.
After 50 days there were 35 worms. Use this information to find a complete equation for the model, giving your value of k k\,k to 3 significant figures.
Use the model to predict the number of worms after one year.
Sketch the graph of W W\,W against ttt.
Practise Edexcel AS Level Maths Exponentials and Logarithms with exam-style questions for AS Level Maths. 41 questions 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, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 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.