Question

In 2000, the population of a town was 46.020. By 2002 wpulation had increased to52,070. Assuming that the towns population is increasing linearly answer the followingquestions.a.What is the population of the town by 2006?

Answer 1

We know that the population increased linearly, so an adequate model for the population P in year t is:

`P(t)=m\cdot t+b`

We know that in 2000 the population is 46,020.

In 2002 the population is 52,070.

This are two points of the line that can be written as (2000, 46020) and (2002, 52070).

Then, we can calculate the slope m as:

`m=(P_2-P_1)/(t_2-t_1)=(52070-46020)/(2002-2000)=(6050)/(2)=3025`

With the slope value we can write the equation in slope-point form:

`\begin{gathered} P-P_0=m(t-t_0) \\ P-46020=3025(t-2000) \\ P=3025(t-2000)+46020 \end{gathered}`

With the linear equation defined like this (we don't need to calculate the y-intercept), we can calculate the population expected for 2006:

`\begin{gathered} P(2006)=3025(2006-2000)+46020 \\ P(2006)=3025\cdot6+46020 \\ P(2006)=18150+46020 \\ P(20060)=64170 \end{gathered}`

Answer: the population in 2006 is expected to be 64,170.