Question

The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.
(A) Predict when the percentage will be 47%.
(B) Predict the percentage in 2005.

Answer 1

Using a linear function, we have that:

a) The percentage will be 47% during the year of 2001.

b) The predicted percentage in 2005 is of 44.97%.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The percentage in 1980 is considered as the initial amount, hence b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by:

m = (50.5 - 58.8)/15 = 0.5533.

Hence the percentage in t years after 1980 is given by:

P(t) = 58.8 - 0.5533t.

Item a:

This is t + 1980, for which P(t) = 47, hence:

P(t) = 58.8 - 0.5533t

47 = 58.8 - 0.5533t.

0.5533t = 11.8.

t = 11.8/0.5533

t = 21.3.

1980 + 21 = 2001, hence the percentage will be 47% during the year of 2001.

Item b:

2005 is 25 years after 1980, hence the percentage is P(25), given as follows:

P(25) = 58.8 - 0.5533x25 = 44.97%.

More can be learned about linear functions at brainly.com/question/24808124

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