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. Show that e50k=0.8e^{50k}=0.8e50k=0.8.
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.
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.