B

Step 1: The population of the city in 1996 = 1.75 million, with annual growth rate of 0.5%.

Step 2: After one year, the population of the city would be (1.75 + 1.75 × 0.5%)million.

Step 3: = 1.75 × 1.005 million[Simplify.]

Step 4: The growth factor is 1.005

Step 5: x = number of years after 1996, y = the population in million[Define.]

Step 6: The population increases exponentially as y = ab^x, where a is the initial population and b the growth factor. [The rate of growth continues.]

Step 7: y = 1.75 × (1.005)^x[As a = 1.75, b = 1.005.]

Step 8: So, the equation y = 1.75 × (1.005)^x models the future growth of the population of the city where x is the number of years after 1996, y is the population in millions at x.

Step 9: For the year 2004, x = 2004 – 1996 = 8

Step 10: The population of the city in the year 2003 is = 1.75 × (1.005)⁸

Step 11: [Simplify.]= 1.82

Step 12: The population of the city in the year 2004 will be about 1.82 million.