Question

in 1990, the rate of change of the world population was approximately 0.09125 billion per year (or approximately 1 million people every four days). the world population was estimated to be 5.3 billion in 1990. write an equation to model the population, p (in billions), in terms of t, where t is the number of years since 1990 (t = 0 corresponds to 1990) a. p = 5.3 + 0.09125t b. p = 5.3t + 0.09125 c. p = -5.3 + 0.09125t d. p = -5.3t + 0.09125 please select the best answer from the choices provided a b c d

Explanation:

Step1: Identify the model type

This is a linear growth model, so the general form is \( P = P_0 + rt \), where \( P_0 \) is the initial population, \( r \) is the rate of change, and \( t \) is time.

Step2: Determine \( P_0 \) and \( r \)

In 1990 (\( t = 0 \)), the population \( P_0 = 5.3 \) billion. The rate of change \( r = 0.09125 \) billion per year.

Step3: Substitute into the model

Substituting \( P_0 = 5.3 \) and \( r = 0.09125 \) into \( P = P_0 + rt \), we get \( P = 5.3 + 0.09125t \), which matches option A.

Answer:

A. \( P = 5.3 + 0.09125t \)