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1.8.7 Reduce y = ax^n and y = ab^x to linear form

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Question 34
i.

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>0

Sketch the graph of log⁡10y\log_{10} ylog10​y against log⁡10x\log_{10} xlog10​x. Clearly label the coordinates of the points of intersection of the graph with the coordinate axes.

[4]
ii.

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 log⁡9N\log_{9} Nlog9​N 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.

[5]

1.8.7 Reduce y = ax^n and y = ab^x to linear form Questions

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  3. /1.8.7 Reduce y = ax^n and y = ab^x to linear form