Two experiments measuring the population of insects are started at the same time. PA=ae0.2tP_A = ae^{0.2t}PA=ae0.2t and PB=be0.15tP_B = be^{0.15t}PB=be0.15t. At the start (t=0t=0t=0) total is 120. After 8 days (t=8t=8t=8) total is 480.
Show that a=50a = 50a=50, to the nearest whole number, and find the value of bbb.
Estimate the total number of insects after 10 days.
Find the day that the number of insects in experiment A exceed the number of insects in experiment B.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.