Edexcel A-Level Mathematics A2 P3.3.3 Use Logarithmic Graphs to Estimate Questions

Practise using logarithmic graphs to turn power and exponential relationships into straight lines and recover constants from gradients.

Exam points

convert log y=mx+c into y=kb^x, rounding constants only when required

[Maximum number: 3]

Figure 1

The line l in Figure 1 shows a linear relationship between $\log _{10} y$ and x.
The line passes through the points (0,1.5) and (-4.8,0) as shown.

Hence, or otherwise, express y in the form $k b^{x}$ , giving the values of the constants k and b to 3 significant figures.

$\log_{10}y=\frac{5}{16}x+1.5\Rightarrow y=10^{\frac{5}{16}x+1.5}$ $y=10^{\frac{5}{16}x}\times 10^{1.5}$ $y=31.6\times 2.05^x$
(3)

M1: Removes logs from $\log_{10}y=mx+c$ .

M1: Correct strategy to obtain k and b.

A1: Correct equation $y=31.6\times 2.05^x$ , no errors seen.

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Edexcel A-Level Mathematics A2 P3.3.3 Use Logarithmic Graphs to Estimate Questions question 1