Much of the earth's photosynthesis occurs in the oceans. The rate of primary production depends on light intensity, measured as the flux of photons (that is, number of photons per unit area per unit time). For monochromatic light, intensity attenuates with water depth according to Beer's Law, which states that I(x) = e−kx, where x is water depth. A simple model for the relationship between rate of photosynthesis and light intensity is P(I) = aI, where a is a constant and P is measured as a mass of carbon fixed per volume of water, per unit time.† Calculate [infinity] P(I(x)) dx 0 .

Relationship between rate of photosynthesis and light intensity is,

P (I) = aI

Explanation:

See attached image

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day