Final answer:
The equation given is a logistic growth model and the number 187.6 represents the limiting value of the population in thousands, indicating that the maximum population the city can reach is 187,600 people.
Step-by-step explanation:
The equation you've provided is a logistic growth model, often used to describe how a population grows and reaches a carrying capacity over time. Looking at the equation y = 187.6 / (1 + 29.4e^(-0.03t)), one can identify several components that relate to population dynamics. The number 187.6 represents the carrying capacity of the population, the maximum number to which the population can grow given environmental constraints and resources. This figure is not the population at any specific time, but rather the limit as time goes on. The presence of e, the base of the natural logarithm, and the negative exponent indicate that this model is an exponential function, modified to show logistic growth.
If we evaluate what each part of the equation means concerning the population size over time:
- The term 187.6 actually represents the limiting value of the population in thousands, so the limiting population would be 187,600 people.
- The 29.4e^(-0.03t) formula gives the relationship between the growth rate and the population size over time. The presence of the term e^(-0.03t) indicates the factor by which the population's growth rate decreases as it approaches the limiting value.
Therefore, the correct interpretation of the value in the equation is: The limiting value of the city population is 187,600 people.