According to Statistics Canada, in 2014 the number of vehicles registered in Canada was 32,600 and in 2018 it was 35,100. Assume that the number of vehicle registrations

Question

According to Statistics Canada, in 2014 the number of vehicles registered in Canada was 32,600 and in 2018 it was 35,100. Assume that the number of vehicle registrations keeps growing in a linear manner.

a) What is the linear equation that gives the number of vehicle registrations in a certain year?

b) What is the estimated number of vehicle registrations for 2021? (Use part (a))

c) In which year there will be 40,725 registered vehicles in Canada?

Answer 1

If it's a linear function then it fits the form "y = mx + b". They give you two data points (2014, 32600) and (2018, 35100). First find the slope using the slope equation m = (y₂ - y₁)/(x₂ - x₁) = (35100 - 32600)/(2018 - 2014) = 2500/4 = 625.

So now the equation is y = 625x + b. To find "b". plug in either one of the data points as (x, y). I'll choose (2014, 32600):

32600 = 625(2014) + b

b = -1226150

So y = 625x - 1226150

To find the number of registrations in 2017, plug in 2017 for "x"

To find which year there will be 40,725 registered vehicles. plug in 40725 for "y"