Word problem

[Brookeneedshelp]

in 1994 the number of households recieving food stamps in the united states was 28.5 million households. in 1998 20.8 million households recieved food stamps ler F(t) represent the number of us households in millions recieving food stamps and t the number of years since 1994

a) find the linear funtion that models the above data i need help is this right ?????

20.8 - 28.5 7.7
1994 - 1998 4 7.7/4 1.925 (f) t = 1.925

b) use the function in question 3 to predict the number os us houeholds receiving food stamps in 2000

(f) (2) = 1.925 (2) + 28.5 = 32.35 million

 

[mmm4444bot]

In this exercise, the variable t represents the number of years since 1994, not the years themselves.

In 1994, t = 0

In 1995, t = 1

In 1996, t = 2

et cetera

Your work sort of looks like an attempt to find the slope of the linear function f, but you made an arithmetic mistake in calculating the difference of the y-coordinates.

20.8 minus 28.5 cannot be a positive number because 28.5 is bigger than 20.8; please try again.

Here are the coordinates of the two given points on the line, for use in the slope formula.

m = (y2 - y1)/(t2 - t1)

(0, 28.5)

(4, 20.8)

After you find the correct slope (m), use the point-slope formula to get the definition for f(t).

y - y1 = m(t - t1)

Of course, we define y = f(t), so these symbols are interchangable.

Do my comments help to ring any bells, for you ?

If you're still stuck, please ask specific questions.

Cheers ~ Mark

 

[Brookeneedshelp]

-7.7/4 so - -1.925 ? oh just 7.7 cuz im not suppoise to use the for 4 right ?

 

[mmm4444bot]

-1.925 is the correct slope.

Have you learned about slope, yet ?

 

[Brookeneedshelp]

yes but the teacher explains everything kinda fast

 

[mmm4444bot]

Formulas, lessons and examples about equations of lines should be in your textbook.

You have m = -1.925, so far.

The slope-intercept form for linear equations is:

y = m*t + b

or, using function notation for the y-variable:

f(t) = m*t + b

Previously, I suggested using the point-slope formula, to get the definition for f, but I changed my mind because I'm not sure you've seen that formula.

Let's find the value of b above (the y-intercept) another way.

We have values for variables t and f(t) at two points. We only need one (t, f(t)) pair.

Let's use values at the point (0, 28.5).

t = 0

f(t) = 28.5

m = -1.925

Substitute these three values for the corresponding variables t and f(t) and for the constant m into the equation below, and solve for b.

f(t) = m*t + b