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 plants when the population was first recorded.
Find the rate of increase in the population 10 weeks after the population was first recorded.
Find the first whole number of weeks after which the number of plants exceeds 300.
104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.