The estimated population of a certain city over time is given in the table below. Answer the questions below to explain what kind of function would better model the data, linear or exponential. }(c) Nimber of Years Since Last Cemass, x & 1 & 2 & 3 & 4 Estimated Population, mathrm(ft)(mathrm(x)) & 66,118 & 77,212 & 88,340 & 99.535 Answer function would better model the data because as mathrm(x) increases, the mathrm(y) values change. The of this function is approximately

To determine whether the data is better modeled by a linear or an exponential function, we need to examine the changes in the population over each year. If the population increases by a constant amount each year, the function is linear. If the population increases by a constant percentage each year, the function is exponential.Let's calculate the differences in population from year to year:From year 1 to year 2: From year 2 to year 3: From year 3 to year 4: Now let's examine these differences:- The change from year 1 to year 2 is .- The change from year 2 to year 3 is .- The change from year 3 to year 4 is .The differences are not constant, but they are very close to each other. This suggests that the population might be increasing approximately linearly. However, to confirm this, we should also check the ratios for an exponential function:From year 1 to year 2: From year 2 to year 3: From year 3 to year 4: The ratios are not constant either, and they are decreasing slightly each year. This suggests that the population is not increasing by a constant percentage each year, which would be indicative of an exponential function.Given that the differences in population are relatively stable and the ratios are not constant, a **linear function** would be a better model for the data. The population seems to be increasing by approximately the same amount each year, rather than by a constant percentage.**Answer: A linear function would better model the data because as increases, the values change by approximately the same amount each year.**