The intensity of light, III lumens, penetrating a deep lake decreases with depth, ddd metres, according to the exponential model:
I=I0kd I = I_0 k^d I=I0kdwhere:
Sketch the graph of III against ddd for a day where the surface intensity I0=1200I_0 = 1200I0=1200.
Given that the light intensity is halved at a depth of 8 metres, show that the constant kkk is approximately 0.9170040.9170040.917004 to 6 decimal places.
On a brighter day, the surface intensity is 5000 lumens. Calculate, to 3 significant figures, the light intensity at a depth of 20 metres.
A specific sensor requires at least 312.5 lumens to operate. If the surface intensity is 2500 lumens, use logarithms to calculate the maximum depth, to the nearest metre, at which the sensor will function.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 202 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
