O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2014 · Q98 Marks

The table shows experimental values of variables x and y. | x | 2 | 2.5 | 3 | 3.5 | 4 | |---|---|-----|---|-----|---| | y | 18.8 | 29.6 | 46.9 | 74.1 | 117.2 |

(i)By plotting a suitable straight line graph on the grid below, show that x and y are related by the equation y = abˣ, where a and b are constants.[4]
(ii)Use your graph to find the value of a and of b.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

[1] B1 for the statement, may be seen or implied in later work, (log y = log a + x log b)
[1] M1 for attempt to draw graph of x against log y (lg y or ln y values from table)
[2] A2,1,0 -1 each error in points plotted
[1] DM1 for attempt to find gradient and equate it to log b, dependent on M1 in (i)
[1] A1 b = 2.5 (allow 2.4 to 2.6)
[1] DM1 for attempt to equate y-intercept to log a or use their equation with their gradient and a point on the line, dependent on M1 in (i)
[1] A1 a = 3 (allow 2.8 to 3.2)

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