The population of a species of plant in a field is modelled using the formula P=50e0.1tP = 50e^{0.1t}P=50e0.1t Where t t\,t is the number of weeks since the population was first recorded.
Write down the number of the plants when the population was first recorded.
Find the rate of increase in the population 10 weeks after the population was first recorded.
Find how many weeks it takes for the number of plants to exceed 300.
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.