Question

Write in calculus notation: The population of a city is shrinking at the rate of 1600 per year. (Let p represent population, and t represent time in years.)

Answer 1

1600 per year

Explanation:

The rate at which the population of a city is shrinking can be represented by the derivative of the population function with respect to time.

Let's use the variable p to represent the population and t to represent time in years.

The population function can be written as p(t).

Since the population is shrinking at a rate of 1600 per year, we can express this using the derivative notation.

The derivative of the population function with respect to time, dp/dt, represents the rate of change of the population over time.

In this case, dp/dt = -1600, since the population is decreasing. The negative sign indicates a decrease in population.

So, in calculus notation, we can write dp/dt = -1600 to represent the fact that the population of the city is shrinking at the rate of 1600 per year

Answer 2

The rate at which the population of a city is shrinking can be represented by the derivative of the population function with respect to time. In this case, the population function is represented by p(t), where p represents the population and t represents time in years.

Given that the population is shrinking at the rate of 1600 per year, we can express this using calculus notation as:

d/dt(p(t)) = -1600

In this notation, d/dt represents the derivative of p(t) with respect to t. The negative sign indicates that the population is decreasing over time.

To summarize, the calculus notation for the statement "The population of a city is shrinking at the rate of 1600 per year" is:

d/dt(p(t)) = -1600