3 mark for review a city planner developed the function p to model the population of a city over the next 25…

3 mark for review a city planner developed the function p to model the population of a city over the next 25 years, where p(t) is the projected population of the city t years from now. according to the model, which of the following gives the rate at which the population of the city will be changing at time t = 5? a p(5) b p(6) - p(4) c p(5)/5 d p(5)

3 mark for review a city planner developed the function p to model the population of a city over the next 25 years, where p(t) is the projected population of the city t years from now. according to the model, which of the following gives the rate at which the population of the city will be changing at time t = 5? a p(5) b p(6) - p(4) c p(5)/5 d p(5)

Answer

Explanation:

Step1: Recall derivative meaning

The derivative of a function $y = f(x)$ represents the rate - of - change of the function with respect to the variable $x$. In the context of the population function $P(t)$, where $P(t)$ is the population at time $t$, the derivative $P^{\prime}(t)$ represents the rate at which the population is changing at time $t$.

Step2: Find rate at $t = 5$

To find the rate at which the population of the city is changing at $t = 5$, we need to evaluate the derivative of the population function $P(t)$ at $t = 5$, which is $P^{\prime}(5)$.

Answer:

D. $P^{\prime}(5)$