The linear equations for modeling the populations of Rhode Island (P_R) and Vermont (P_V) after the year 2000 are:
[ P_R = 0.005t + 1.05 ]
[ P_V = 0t + 0.63 ]
Here, t represents the time in years after 2000, and the slopes are rounded to one decimal place.
To model the linear relationship between population (P) and time (t) for Rhode Island and Vermont after the year 2000, we can use the equation P_R = mt + b_R for Rhode Island and P_V = nt + b_V for Vermont. Here, m and n represent the slopes, and b_R and b_V represent the y-intercepts.
Given that the population of Rhode Island in 2010 was 1.05 million and in 2020 was 1.06 million, we can use these data points to find the slope m. Using the formula m = (P_2 - P_1) / (t_2 - t_1), where P_1 is the population in 2010, P_2 is the population in 2020, t_1 is the corresponding time in years, and t_2 is the time in years, we calculate the slope for Rhode Island.
Similarly, using the population data for Vermont in 2010 (0.63 million) and 2020 (0.63 million), we can find the slope n for Vermont.
The final linear equations are:
[ P_R = 0.005t + 1.05 ]
[ P_V = 0t + 0.63 ]
Here, t represents the time in years after 2000, and the slopes are rounded to one decimal place.