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Sagot :
Using a linear function, we have that:
- The percentage will be 47% during the year of 2001.
- The predicted percentage in 2005 is of 44.97%.
Given that, 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.
What is a linear function?
Linear functions are those whose graph is a straight line. The standard form of the linear function is f(x)=y= mx + b. A linear function has one independent variable and one dependent variable.
Where, 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, so 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.
Thus, the percentage in t years after 1980 is P(t) = 58.8 - 0.5533t.
Now, t + 1980, for which P(t) = 47.
So, 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, so the percentage will be 47% during the year 2001.
Now, 2005 is 25 years after 1980, so the percentage is P(25), given as follows: P(25) = 58.8 - 0.5533x25 = 44.97%.
More can be learned about linear functions at https://brainly.com/question/21107621.
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