Small Breweries  U.S. craft-beer breweries (breweries that make fewer than 6 million barrels annually and are less than 25% owned by big breweries) have been doing booming business. The number of these small breweries from 2008 through 2012 can be modeled by using a quadratic function of the form f(t) = at2 + bt + c where a, b, and c are constants and t is measured in years, with  t = 0  corresponding to 2008.† (a) Find a, b, and c if  f(0) = 1547,   f(2) = 1802,  and  f(4) = 2403. a  =    b  =    c  =    (b) Use the model obtained in part (a) to estimate the number of craft-beer breweries in 2016, assuming that the trend continued. (Round your answer to the nearest integer.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 33E
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Small Breweries

 U.S. craft-beer breweries (breweries that make fewer than 6 million barrels annually and are less than 25% owned by big breweries) have been doing booming business. The number of these small breweries from 2008 through 2012 can be modeled by using a quadratic function of the form
f(t) = at2 + bt + c
where ab, and c are constants and t is measured in years, with 
t = 0
 corresponding to 2008.†
(a)
Find ab, and c if 
f(0) = 1547,
 
f(2) = 1802,
 and 
f(4) = 2403.
a  =   
b  =   
c  =   
(b)
Use the model obtained in part (a) to estimate the number of craft-beer breweries in 2016, assuming that the trend continued. (Round your answer to the nearest integer.)
 
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