Question

May I please have some help? I'm about to cry!

Some scientists are trying to make a cable for which the intensity of light would decrease by 5 lumens per unit length of the cable. Can this situation be represented by a linear function? Justify your answer and write the appropriate function to represent this situation if 1500 lumens of light enter the cable. (4 points)

I know that the formula is f(x) = 3.4x + 1,500

Answer 1

sites acting odd at the moment

Answer 2

Can you see it though?

Answer 3

if it deacreases by 5 for every unit of length, then the f(x) is off

Answer 4

1500 to start with, and -5 for every x unit in length

1500 - 5x is what i see it as

Answer 5

So, now I solve it and I get...(solving it)

Answer 6

300 = x

Answer 7

not sure what you are solving for, all your post says is to develop a function

Answer 8

Oh, whoops!

Answer 9

but yes, when x = 300, there is 0 lumnes

Answer 10

So, for the first question, it is NOT a linear equation. Why?

Answer 11

without knowing what a lumen actually is; the information does present a linear fashion. it decreases by 5 for every 1 increase.

-5/1 is a slope; and is constant

Answer 12

how do you define a linear function?

Answer 13

f(x) = mx + b

Answer 14

Dear Grama: As we didn't start with an equation (involving " = "), there's nothing to solve for. Instead, we're to decide whether or not a LINEAR MODEL is appropriate to represent the physical situation given.

f(x) = 3.4x + 1,500 is an example of a LINEAR MODEL. Strictly speaking, it's not an equation, but a formula.

This formula would fit this situation perfectly if we replace that +3.4 by -5 (since 5 lumens are lost per unit length of the cable: f(x) = -5x + 1500 lumens.

Answer 15

then -5x + 1500 is a suitable format

Answer 16

I agree. Let's just give the function a name.

Answer 17

Okay, I was thinking it should be like that at first, but then I got it mixed up!

Okay, so, it CAN be represented by a linear function; -5x +1,500. What about the second part? :-)

Answer 18

All you really need to "justify your answer" is already included in the above discussion. We're writing a formula/function for the amount of light, measured in lumens, at any distance x from the starting point. We start out at x=0, at which point the number of lumens is 1500 (the y-intercept of the graph), and subtract 5x lumens to obtain the amount of light (in lumens) that could be measured at each point on the graph, up to x = 300.
Think: why can't x exceed 300?

Answer 19

mathmale has this .. i got stuck in the br

Answer 20

Hmmm.....I-oh! Because when we multiply 300 lumens by 5 we get 1,500!

Answer 21

Thank you both for the help!