Question

1. the world population from 2000 and projected to 2050, in billions, is given by the function y = 0.063x + 6.191, where x is the number of years after 2000 (source: u.s. census bureau). what is the rate of change of this growth? include units in your answer.

Explanation:

Step1: Identify the function type

The population function is $y = 0.063x+6.191$, which is a linear - function of the form $y = mx + b$.

Step2: Recall the derivative of a linear function

The derivative of a linear function $y=mx + b$ with respect to $x$ is $m$. Here, $m = 0.063$. The derivative of a function represents the rate of change of the function.

Answer:

The rate of change of the population growth is $0.063$ billion people per year.