An oceanographer is studying how light intensity decreases at different depths in the ocean. For a specific location, the light intensity, \(I\) (in lumens), at a depth of \(d\) meters is modelled by the formula \(I=Pe^{-kd}\), where \(P\) and \(k\) are constants. The table below shows corresponding values of \(d\) and \(I\). It is believed that an error was made in recording one of the values of \(I\).
| \(d\) (metres) | \(2\) | \(4\) | \(6\) | \(8\) | \(10\) |
|---|
| \(I\) (lumens) | \(122\) | \(74\) | \(30\) | \(27\) | \(17\) |
Explain how a straight line graph can be drawn to represent the formula and draw it for the given data.[4]
Using your straight line graph,
identify the incorrect reading and suggest a corrected value for \(I\),[2]
estimate the value of \(k\), and[2]
deduce the value of \(P\).[2]