Question

A city had a population of 30,000 people in the year 2010. The table models the population, y, after a given number of years, x. x (years) 0 1 2 3 4 y (population) 30,000 39,000 50,700 65,910 85,863 Which type of model would best fit the data, and why? Linear, because the population is increasing by 30% each year Linear, because the population is decreasing by 30% each year Exponential growth, because the population is increasing by 30% each year Exponential decay, because the population is decreasing by 30% each year

Answer 1

To determine the type of model that best fits the given data, we can analyze the population growth pattern over the years.

In this case, we can calculate the percent increase in population from year to year. Let's calculate the percentage increase for each consecutive pair of years:

Year 0 to Year 1: (39,000 - 30,000) / 30,000 ≈ 0.3 (30% increase)
Year 1 to Year 2: (50,700 - 39,000) / 39,000 ≈ 0.3 (30% increase)
Year 2 to Year 3: (65,910 - 50,700) / 50,700 ≈ 0.3 (30% increase)
Year 3 to Year 4: (85,863 - 65,910) / 65,910 ≈ 0.3 (30% increase)

As we can see, the population is increasing by approximately 30% each year. This growth pattern is indicative of exponential growth, not linear growth. Therefore, the type of model that best fits the data is exponential growth because the population is increasing by 30% each year.