The variables xxx and yyy are connected by the relationship
y=10−15x2.5,x>0 y = \frac{10^{-15}}{x^{2.5}}, \quad x > 0 y=x2.510−15,x>0Sketch the graph of log10y\log_{10} ylog10y against log10x\log_{10} xlog10x. Clearly label the coordinates of the points of intersection of the graph with the coordinate axes.
A population of microbes NNN increases over time ttt hours according to the model N=abtN = ab^tN=abt, where aaa and bbb are positive constants. A scientist plots the linear relationship between log9N\log_{9} Nlog9N and ttt. The resulting line has a positive gradient and passes through the points (0,2.5)(0, 2.5)(0,2.5) and (−10,0)(-10, 0)(−10,0). Determine the exact values of aaa and bbb.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.