In a bacterial culture the population (in thousands) depends on nutrient…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

In a bacterial culture the population

P

(in thousands) depends on nutrient concentration

C

(in mg/L) through

P = 200\sqrt{C} + 50

. At an instant when

C = 16\,\text{mg/L}

, the concentration is falling at the rate

\dfrac{dC}{dt} = -0.3\,\text{mg L}^{-1}\text{h}^{-1}

. Determine the instantaneous rate of change

\dfrac{dP}{dt}

at that instant.