Question

The estimated population of a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential. 27909 23672

Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
27909
23672
19401
15151

Box 1: Linear or Exponential?
Box 2: Additively or Multiplicatively?
Box3: Common difference or common ratio
Box4: Answer to box 3

Answer 1

A linear function would better model the data because as x increases, the y values change additively, The common difference of the function is approximately 4253

Explanation:

A linear function would better model the data because as x increases, the y values change additively,

(e.g, x from 1 to 2, so, y from 27909 to 23672

The difference is 27909 - 23672 = 4237

from 2 to 3, 23672 to 19401 with difference 23672 - 19401 = 4271

from 3 to 4, 19401 to 15151 with difference 19401 - 15151 = 4250)

The common difference of this is approximately, we use average of all the differences we have found above, so,

Average difference = (4237 + 4271 + 4250)/3 = 4253

The approximate common difference is 4253