Question

A company manufactures an alarm clock. Three weeks ago the company had 250 on hand, two weeks from not it will have 500, assume the company will continue to make clocks at this same rate.

What is the expression for this word problem?
The number of clocks starts at 400 how does it increase as x increases?

Answer 1

Ummm... We're just making them for fun? No selling?

Answer 2

There isn't anything about selling just inventory increasing.

Answer 3

Doesn't quite make sense. Consider these three sequential pieces of information:

1) The number of clocks starts at 400
2) Three weeks ago the company had 250 on hand
3) two weeks from not it will have 500

If we're JUST manufacturing, that can't happen. Did you copy the problem exactly correctly?

Answer 4

Perhaps:

t = 0 is right now and t is in weeks.

f(-3) = 200
f(+2) = 500
Find t0 such that f(t0) = 400

That might be an interesting question, but I moved the 400 to a place BETWEEN 200 and 500.

Answer 5

Nice try. It won't load.

Answer 6

it wont let me copy and paste :(

Answer 7

1. how many clocks does the company currently have?
2. In how long will the company have 650 clocks?
3. In one more year, how many clocks will the company have?
4. If the company needs a total of two thousand clocks, in how many weeks from now will it have this amount?
To write the expression, variable for the time, in weeks, from today and use the variable to write a rule for the number of clocks manufactured

Answer 8

does this help a little better? I just can't figure put how to write the expression

Answer 9

Unfortunately, it's not perfectly clear what's going on. The "400" just doesn't fit in. I thin k "at this same rate" might suggest a linear relationship, but I'm just not very comfortable with it.

Anyway, we still have.

f(-3) = 200
f(+2) = 500

This might suggest that we get 300 clocks in 5 weeks. Do you see that?
Another way to say 300 clocks in 5 weeks is 60 clocks per week. It's the same ratio or proportion:

\(\dfrac{300\;clocks}{5\;weeks} = \dfrac{60\;clocks}{1\;week}\)

This,

"A" is some starting value and 60 / week is the rate.

f(-3) = A - 3(60) = A - 180 = 200, So A = 380
Finally, F(Weeks) = 380 + 60(Weeks)

Let's see if it works: F(2) = 380 + 60(2) = 380 + 120 = 500 -- Perfect.

Now, we can answer all the other questions.

Just building the linear function to hit the two known points is the super-cool part.

Answer 10

the 400 is at zero weeks, they have 400 clocks

Answer 11

Right, that what it says, but that doesn't make any sense with a linear model.

(-3,200)
(0,400)
(2,500)

These are NOT colinear. There is NOT one line that hits all three of these.