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Regression, Correlation and Hypothesis Testing

Regression, Correlation and Hypothesis Testing

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Question 140

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=I0​kd

where:

  • I0I_0I0​ is the intensity of light at the surface.
  • kkk is a constant, with 0<k<10 < k < 10<k<1.
  • ddd is the depth below the surface in metres.
a.

Sketch the graph of III against ddd for a day where the surface intensity I0=1200I_0 = 1200I0​=1200.

[2]
b.

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.

[2]
c.

On a brighter day, the surface intensity is 5000 lumens. Calculate, to 3 significant figures, the light intensity at a depth of 20 metres.

[2]
d.

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.

[3]
Markscheme

Regression, Correlation and Hypothesis Testing Questions

  1. A Level
  2. /Maths
  3. /Regression, Correlation and Hypothesis Testing

202 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.

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