The growth in the population of worms, WWW, is modelled by the equation: W=95−75eatW = 95 - 75e^{at}W=95−75eat where a a\,a 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 k k\,k days there were 35 worms, where k>0k>0k>0. Use this information to find a complete equation for the model, giving your value of a a\,a in terms of kkk.
Use the model to predict the number of worms after one year, in terms of kkk.
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.