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.