Final answer:
The correct formula for the population of the town in terms of years since 1920 is P = 2600 - 50t, representing a linear decrease of 50 people per year from an initial population of 2600 people in 1920, which aligns with option (a).
Step-by-step explanation:
To find a formula for the population (P) of the town in terms of years since 1920 (t), we must first determine the rate of change of the population per year. Since the population decreased from 2600 in 1920 to 2350 in 1925, this is a decrease of 2600 - 2350 = 250 people over 5 years. Therefore, the yearly decrease is 50 people per year.
The formula for a linear relation is of the form P = mt + b, where m is the slope and b is the y-intercept. Here, m is -50 since the population decreases by 50 every year, and b is 2600 since that was the population at t = 0 (the year 1920).
Substituting these values into the linear formula, we get P = 2600 - 50t. Thus, the correct formula is P = 2600 - 50t, which corresponds to option (a).