The intensity I I\,I of radiation at a distance d d\,d from a source is modeled by the equation
I=109d3,d>0 I = \frac{10^9}{d^3}, \quad d > 0 I=d3109,d>0Sketch the graph of log10I\log_{10} Ilog10I against log10d\log_{10} dlog10d. Show on your sketch the coordinates of the points of intersection of the graph with the axes.
A biologist monitors the growth of a bacterial colony. The relationship between the population size P P\,P and time ttt (in hours) is represented by a linear relationship between log5P \log_5 P\,log5P and ttt. The graph of log5P \log_5 P\,log5P against t t\,t is a straight line passing through the points (0,2)(0, 2)(0,2) and (−10,0)(-10, 0)(−10,0). Show that P=abtP = ab^tP=abt where a a\,a and b b\,b are constants to be found.
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.