Question

The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 110I I2 + I + 4 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum? I = thousand foot-candles

Answer 1

Using the vertex of a quadratic equation, it is found that P is at a maximum for l = -0.5 thousand foot-candles.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

$x_v = -\frac{b}{2a}$

$y_v = -\frac{b^2 - 4ac}{4a}$

Considering the coefficient a, we have that:

• If a < 0, the vertex is a maximum point.

• If a > 0, the vertex is a minimum point.

In this problem, the function for P is given by:

$P(l) = \frac{110l}{l^2 + l + 4}$

The function will be at a maximum when the denominator is at a minimum. The denominator is a quadratic function with coefficients a = 1, b = 1, c = 4, hence:

$l_v = -\frac{b}{2a} = -\frac{1}{2} = -0.5$

P is at a maximum for l = -0.5 thousand foot-candles.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

#SPJ1