SOLUTION: The average price p (in thousands of dollars) of a new mobile home in the United States from 1974 to to 1993 can be approximated by the piecewise-defined model: p(t)= {19.247+1.20

Question 802403: The average price p (in thousands of dollars) of a new mobile home in the United States from 1974 to to 1993 can be approximated by the piecewise-defined model:
p(t)= {19.247+1.204t -6≤t≤-1}
{19.305+0.496t+0.0116t^2 0≤t≤13}
where t= 0 represents 1980.
Find the average price of a mobile home in 1978.
Answer in units.
I do not understand how to do this problem and if someone can explain it to me, much is appreciated.
Answer by homeworkhedgehog(9) (Show Source): You can put this solution on YOUR website!
A piecewise function is a function that has more than one section to it, like if you combined different spliced different functions together at a certain point.
In this problem, the first function () is graphed over the section where t is between -6 and -1 only. The second function () is then graphed over its own section (from 0 to 13) on the t-axis (x-axis).
This function tells you the average price of a home in a given year, t, and it wants to know how much it would be in the specific year, 1978. When they tell us that t=0 represents 1980, that gives us a frame of reference. So now we know that t=1 would be the next year, 1981; t=2 would be 1982; and so on. We can use this to work backwards as well. So t=-1 would be 1979, and t=-2 would be 1978.
Now we have information that will be used in answering the question: t=-2 (for 1979), and the function that is applicable to the position t=-2 () because -2 is between -1 and -6, so this is the "piece" of our piecewise function that we use.
Plugging -2 into , we get , which is our answer in thousands of dollars. So there you have it, the average price of a mobile home in '78 was $16,839.

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