The intensity of light, $I$ lumens, penetrating a deep lake decreases with depth, $d$ metres, according to the exponential model:

I = I_0 k^d

where:

$I_0$ is the intensity of light at the surface.
$k$ is a constant, with $0 < k < 1$ .
$d$ is the depth below the surface in metres.

Sketch the graph of $I$ against $d$ for a day where the surface intensity $I_0 = 1200$ .

Given that the light intensity is halved at a depth of 8 metres, show that the constant $k$ is approximately $0.917004$ 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.

The intensity of light, $I$ lumens, penetrating a deep lake decreases with depth, $d$ metres, according to the exponential model:

I = I_0 k^d

where:

$I_0$ is the intensity of light at the surface.
$k$ is a constant, with $0 < k < 1$ .
$d$ is the depth below the surface in metres.

Sketch the graph of $I$ against $d$ for a day where the surface intensity $I_0 = 1200$ .

Given that the light intensity is halved at a depth of 8 metres, show that the constant $k$ is approximately $0.917004$ 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.

1.6.8 Reduction to linear form

Question 33

Markscheme

1.6.8 Reduction to linear form

Question 33

Markscheme

1.6.8 Reduction to linear form

Question 33

1.6.8 Reduction to linear form Questions

1.6.8 Reduction to linear form

Question 33

1.6.8 Reduction to linear form Questions