Question

In t years, the population of a certain city grows from 600,000 to a size P given by P(t) = 600,000 + 4000t² . Find the growth rate,

Answer 1

The growth rate can be found by taking the derivative of the population function, P(t).

Step-by-step explanation:

The growth rate can be found by taking the derivative of the population function, P(t). The growth rate represents the rate at which the population is increasing over time.

To find the growth rate, we differentiate the population function P(t) = 600,000 + 4000t² with respect to t.

P'(t) = 0 + 8000t = 8000t

So, the growth rate is 8000t.

The growth rate is the expression we found for P'(t), which is 8000t at time t.

Therefore, the growth rate of the city's population at time t is 8000t people per year.