Based on the given data in the problem, you write the function

    A(t) = 931.8 - 3.27*t 

for acres in use (in millions acres), where t is the time, in years, after 1997.


By making it, you   that  the average rate remains the same after 1997.  

So, your  "prediction" equation is 


    931.8 - 3.27*t = 915.


From this equation, you find t, the time in years after 1997

    t = .


Then you use your calculator and find  t = 5.13  years.


It means that this area of 915 millions acres in use will be reached in the year 1997 + 5 = 2002.


ANSWER.  The prediction is the year 2002.

hello! i need help! i am trying to solve a word problem but i can't figure it out! the word problem is: "the number of acres of farmland in the US has decreased at a relatively constant rate of 3.27 million acres per year from 1987 to 1997. in 1997, there were 931.8 million acres of farmland." i have to write an equation that gives the number of acres of farmland as a function of the number of years since 1987. then i have to predict when the number of acres will fall below 915 million acres.

Initial year: 1987, which is treated as YEAR 0. Coordinate point: (0, y1). 
Subsequent year: 1997, which is 10 YEARS after 1987, the initial year. Coordinate point (10, 931.8), or (x5, y2). 

To get your equation, you can use the SLOPE-INTERCEPT form of a linear equation, which is: y = mx + b. Substitute (10, 931.8) for (x, y), and then find the y-intercept, which is also the INITIAL number of acres from the INITIAL year, 
1987

OR  

Simply use the POINT-SLOPE form of a linear equation, which is: 
   y - y2 = m(x - x2)  
  y - 931.8 = - 3.27(x - 10) ------ Substituting 931.8 for y2,, - 3.27 for m (slope), and 10 for x2
y - 931.8 = - 3.27x + 32.7
        y = - 3.27x + 32.7 + 931.8 ----- Adding 931.8 to both sides
        y = - 3.27x + 964.5 <===== Requested EQUATION

As a prediction is required for the year the number of acres will fall below 915 million acres, 
the requested EQUATION, y = - 3.27x + 964.5 becomes the following INEQUALITY:
- 3.27x + 964.5 < 915 
          - 3.27x < 915 - 964.5 
          - 3.27x < - 48.5
                   ---- Changing INEQUALITY to its OPPOSITE, since we're DIVIDING by a negative value 
                  x > 15.1376147.
With x being greater than (>) 15.1376147, x = 16 years. So, predicted year after 1987 that the number of acres
will fall below 915 million acres is 2003 (1987 + 16).

You can do the CHECK!!