Question

The intensity of light energy under water decreases rapidly. Many factors affect how quickly the intensity decreases. The light energy under water can be calculated using an exponential relation. For example, Ocean: I=325×(1.024)dI = 325 \times ( 1.024 ) ^ { - d } Lake Erie: I=401×(1.222)dI = 401 \times ( 1.222 ) ^ { - d } In these relations, d is the depth, in metres, and I is the light energy, in langleys. a) Why is a negative exponent used in the formulas? b) Sketch a graph of each relation. c) In which body of water does the intensity decrease more quickly? Explain why.

Solution

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a)\textbf{a)}

Negative exponents were used because the intensity of light decreases as the depth is increasing.

b)\textbf{b)}

Use a table of values or a graphing calculator to obtain the graphs as shown:

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