Question

Find the rate at which the level of pollutant is increasing when the population of the community is 16,000. If P(t) represents the population at time t and C(t) represents the pollutant concentration, which expression represents the required rate?

a) dC/dt * P(t)
b) C(t) / dP/dt
c) dC/dt / P(t)
d) P(t) * dC/dP

Answer 1

The rate at which the level of pollutant is increasing for a population of 16,000 is best represented by the expression P(t) * dC/dP, utilizing the principles of calculus and taking into account the direct proportionality to the population size.

Step-by-step explanation:

The student is looking to find the rate at which the level of pollutant is increasing when the population of the community is 16,000. To find this rate, we need to use the concept of derivatives from calculus. The rate of change of the pollutant concentration with respect to time (dC/dt) is affected by the population size. If the rate of change of concentration is directly proportional to the population size, the correct expression to represent the rate at which the level of pollutant is increasing would be the rate of change of pollutant concentration with respect to population multiplied by population itself, or P(t) * dC/dP. Therefore, the correct answer is option d).