Final answer:
The initial population value P₀ in the population growth equation is 180,000 at time t=0. Since P₀ is what the question asks for, the answer is simply the given initial population without any calculations. The correct option is a. 180,000.
Step-by-step explanation:
The problem you've provided is centered around the exponential growth formula, which is used to model population growth over time. The general form of the equation is P = P₀(1+r)^t, where P represents the future population, P₀ is the initial population, r is the growth rate (expressed as a decimal), and t is time in years.
In this scenario, the initial population (P₀) of the city is given as 180,000 at time t=0, which is commonly the starting point for time in such models. Since the growth rate is 5% per year, we express this as r=0.05. Over the course of 3 years, the growth rate is applied each year. However, the question is asking for the value of P₀, which is already provided as the initial population.
Therefore, the value of P₀ is simply the initial population at t=0, which is 180,000. This corresponds to option a. 180,000, which is the correct answer.