Answer to Question #287725 in Algebra for austyn

Question

The average annual number of cigarettes smoked by an adult in some country continues to decline. For the years 2000−​2012, the equation y=−77.8x+2051 approximates this data.​ Here, x is the number of years after​ 2000, and y is the average annual number of cigarettes smoked. If this trend​ continues, find the year in which the average annual number of cigarettes smoked reaches zero. To do​ this, substitute 0 for y in the equation and solve for x.

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Part 1

In

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​, the average annual number of cigarettes smoked will be zero.

​(Round down to the nearest​ year.)

Answer 1

Substituting 0 for y in the equation, we attain,

$0=-77.8x+2051$

add 77.8x on both sides to attain

$77.8x=2051$

divide both sides by 77.8

$x=26.36$

nearest year, we have

$x=26 years$