Question 1203958: 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.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! Application of linear equation
Points (x,y) for time in years x and amount of farmland y
 , may be the form of equation of choice.
THE SLOPE m, IS GIVEN AS 3.27 million acres per year, and is negative.
You can let year 1987 be assigned time 0 and you are given a point (10,931.8).
That should be enough for you to continue the rest of the way.
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Notice you need to read the description very carefully.
Time 0 can be year 1987;
and time 10 would be year 1997.
The amount of farmland was 931.8 million acres IN YEAR 1997, which is at x=10.
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One might be more confortable using point-slope equation form.
and put this into slope-intercept form.
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
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.
~~~~~~~~~~~~~~~~~~~~~~~~~
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.
Solved.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
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!!
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