The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function p = 120i i2 + i + 9 where i is the light intensity (measured in thousands of foot-candles). for what light intensity is p a maximum?

The given function is:

P = 120 i / (i^2 + i + 9)

or

P = 120 i (i^2 + i + 9)^-1

The maxima point is obtained by taking the 1st derivative of the function then equating dP / di = 0:

dP / di = 120 (i^2 + i + 9)^-1 + (-1) 120 i (i^2 + i + 9)^-2 (2i + 1)

setting dP / di =0 and multiplying whole equation by (i^2 + i + 9)^2:

0 = 120 (i^2 + i + 9) – 120i (2i + 1)

Dividing further by 120 will yield:

i^2 + i + 9 – 2i^2 – i = 0

-i^2 + 9 =0

i^2 = 9

i = 3      (ANSWER)

Therefore P is a maximum when i = 3

Checking:

P = 120 * 3 / (3^2 + 3 + 9)

P = 17.14

The problem here is that according to aufbau principle before 3d orbital 4s subshell comes.after filling 3p orbital with electrons you have 4 electrons left, you place two in 4s with opposite spin and the other two in 3d in any of its two orbitals of total five orbitals with the same spin.

Sorry i think the answer is b