Question

Question 4A small town had 425 homes in 2018, and by 2020, this had grown to 525.(a) Assuming the number of homes is growing linearly, find the growth rate d.(b) Write a linear model of the form Pt=P0+dt to describe the number of homes in this town from 2018 onward.Pt = (c) Predict how many homes there will be in this town in 2026. homes(d) When do you expect the number of homes to exceed 675? Give your answer as a calendar year (ex: 2020).During the year

Answer 1

(a) Use the following formula:

`d=(P_2-P_1)/(t_2-t_1)`

where:

P2 = 525

P1 = 425

t2 = 2020

t1 = 2018

Replace the previous values into the expression for d:

`d=(525-425)/(2020-2018)=(100)/(2)=50`

Hence, the growth rate is 50 homes per year.

(b) Due to you can take t = 0 for the counting of homes from 2018, you can write the following linear equation:

`P(t)=425+50t`

(c) Replace t = 2026 - 2018 = 8, into the expression for P(t):

`P(8)=425+50(8)=425+400=825`

There will be 825 homes in 2026.

(d) Replace P(t) = 675 and solve for t:

`\begin{gathered} 625=425+50t \\ 625-425=50t \\ 200=50t \\ (200)/(50)=t \\ t=4 \end{gathered}`

Then, by considering that 2018 is for t = 0, you have for t = 4:

2018 + 4 = 2022

During the year 2022 the number of homes will exceed 675 homes.