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.
62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.