Question

1. The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 56.1% in 1990 to 51.3​% in 2005.

a. Predict when the percentage will be 42​%.

b. Predict the percentage in 2014.

Answer 1

Soln :

We can see that this is a linear model, as the decrease in percentage of the consumers under 50 years of age changes linearly.

A linear model is an equation that describes the relation between two quantities that show a constant rate of change. The equation has the following form :

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It is given that the percentage of automobile consumers under 50 years of age dereased linearly from 56.1% in 1990 to 51.3% in 2005.

We can see that as the years go by the percentage of consumers under 50 years of age decreases.

So let x = time in years

          y = Percentage of automobile consumers under 50 years of age in that respective year.

Then , When x = 1990 ; y = 56.1

                      x = 2005 ; y = 51.3

Substitute these values into the equation.

...............................(1)

...............................(2)

(1) - (2) :

Then Substitute A = - 0.32 in (1) :

Then the equation is

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Now to predict when the percentage will be 42, substitute y = 42

Then,   

             

                     

So the percentage will be 42 in the year 2034.

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Now to predict what the percentage will be in 2014, substitute x = 2014

So in 2014, the percentage of consumers = 48.4

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