Edexcel IAL Mathematics P3.3.3 logarithmic graphs

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.

$\log_{10}y=\frac{5}{16}x+1.5\Rightarrow y=10^{\frac{5}{16}x+1.5}$

M1

$y=10^{\frac{5}{16}x}\times 10^{1.5}$

M1

$y=31.6\times 2.05^x$

A1

(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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P3.3.3 - Use logarithmic graphs to estimate question 1