Question

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.

number of years since last census, x	1	2	3	4
estimated population, (y)	42,438	41,776	40,684	39,841

Explanation:

Step1: Calculate differences for linear - check

Find the differences in population values.
$42438 - 41778=660$, $41778 - 40684 = 1094$, $40684-39841 = 843$. The differences are not constant.

Step2: Calculate ratios for exponential - check

Find the ratios of consecutive population values.
$\frac{41778}{42438}\approx0.9844$, $\frac{40684}{41778}\approx0.9738$, $\frac{39841}{40684}\approx0.9793$. The ratios are approximately constant.

Answer:

Exponential function would better model the data.