Question 190124This question is from textbook Mathmatics with Applications
: According to the data from the U.S. department of Agriculture, the annual per capita consumption of red meat in the US has declined in a linear fashion from 131.7 pounds in 1970 to 107.7 in 2000.
a. Let x=0 correspond to 1900 and find the rule of a linear function that gives the approximate annual per capita consumption of red meat in year x.
b. If this trend continues in what year will per capita consumption be 100 pounds?
This question is from textbook Mathmatics with Applications
Answer by cutepiscean5(19)   (Show Source):
You can put this solution on YOUR website! (a) let the years denote the x-coordinates and the consumption of red meat be denoted by the y-coordinates, then we are given the following coordinates:
Since, year 1900 corresponds to x = 0, the year 1970, will correspond to x = 70. so when x = 70, y = 131.7 pounds. The point can be represented as
(70,131.7)
similarly, when year is 2000, then x = (2000 - 1900) = 100. so we have
(100, 107.7) as another coordinate in our xy-system.
now since we have two points, using the point-slope formula we can determine the linear equation as:
thus the equation becomes:
=> 
=> 
=> 
=> 
=>  -- this is the rule.
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(b)
we are given y = 100 pounds, we need to determine that value of x for which y = 100 pounds. We plug this value of y in our equation.
=> 
=> 
=> 
we can take x approx as 102. so the year would be 
Hope this helps.
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