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.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 202 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
