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Explanation:
This is a geometric sequence because each new term is found by multiplying the last term by -4.
The common ratio is r = -4. The first term is a = -9. We want to sum up n = 9 terms.
Use the geometric nth partial sum formula below to plug in the terms mentioned
9514 1404 393
Answer:
(a, b, c) = (-0.425595, 11.7321, 2.16667)
f(x) = -0.425595x² +11.7321x +2.16667
f(1) ≈ 13.5
Step-by-step explanation:
A suitable tool makes short work of this. Most spreadsheets and graphing calculators will do quadratic regression. All you have to do is enter the data and make use of the appropriate built-in functions.
Desmos will do least-squares fitting of almost any function you want to use as a model. It tells you ...
a = -0.425595
b = 11.7321
c = 2.16667
so
f(x) = -0.425595x² +11.7321x +2.16667
and f(1) ≈ 13.5
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<em>Additional comment</em>
Note that a quadratic function doesn't model the data very well if you're trying to extrapolate to times outside the original domain.
