Question

Environmental scientists measure the intensity of light at various depths in a lake to find the "transparency" of the water. Certain levels of transparency are required for the biodiversity of the submerged macrophyte population. In a certain lake the intensity of light at depth x is given by I=3.2e?0.6x where I is measured in lux (a measure of light intensity) and x in cm. a) Find the intensity at a depth of 6 cm

Answer 1

To calculate the light intensity at 6 cm depth using the formula I = 3.2e^-0.6x, plug in x = 6, then compute e^-3.6 and multiply by 3.2 to obtain the value of I. This is crucial for understanding water transparency and maintaining biodiversity in aquatic ecosystems.

Step-by-step explanation:

To find the intensity of light at a depth of 6 cm in a lake using the given formula I=3.2e-0.6x, where I is the intensity in lux and x is the depth in cm, substitute x with 6:

I = 3.2e-0.6×6

Now calculate the exponent:

I = 3.2e-3.6

Next, use a calculator to find the value of e-3.6 and multiply it by 3.2 to get the final intensity I.

It is important for environmental scientists to understand the transparency of water for the maintenance of biodiversity, especially for submerged macrophyte populations, which rely on sufficient light intensity for photosynthesis.