# 1. The percentage of automobil

1**. The percentage of automobile consumers who are under50 years of age decreased approximately linearly from 56.1% in 1990to 51.3% in 2005.**

**a.** Predict when the percentage will be42%.

**b.** Predict the percentage in 2014.

Answer:

**Soln :**

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

**A linear model is an equation that describes therelation between two quantities that show a constant rate ofchange. The equation has the following form :**

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It is given that the percentage of automobile consumers under 50years of age dereased linearly from 56.1% in 1990 to 51.3% in2005.

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

So let x = time in years

y =Percentage of automobile consumers under 50 years of age in thatrespective 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 year2034.**

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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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