Section 2.1: Linear Models

Question

Question 4:

A 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 .

(b) Write a linear model of the form  to describe the number of homes in this town from 2018 onward.

 =   

(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) 50 per year growth

50/425 = 2/17 = about 12% annual growth rate

but 50/475 = 2/19 = about 11%

annual growth rate declines annually,

but you want d= 50

b) Pt = Po +dt = 450 + 50t

c) Pt + 450 + 50(8) = 850

d) 675 = 450 +50t

50t = 225

t = 225/50 = 9/2 = 4.5 + 2018 = 2022 about June