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### Course: Algebra (all content)>Unit 3

Lesson 13: Constructing linear models for real-world relationships

# Linear functions word problem: iceberg

Sal is given a verbal description of a real-world relationship involving a melting iceberg, and is asked to find the formula of the function that represents this relationship.

## Want to join the conversation?

• The notation confuses me.
I have always thought of parenthisis as multiplication. So S(0) should be zero.
Just like 2(x+1) = 2x+2
What do I have to put into my brain to make this make sense to me?
• You REALLY need to get used to the meaning of parenthesis with respect to context that they are being used.
If I say, what is "f(2)" I want to know the output value of function f with the input value 2.
If I am told there is a function called S(t) and I am asked, what is the value of the function S when t=0, then I write S(0). In these cases, functional notation is the context, so f or S is the name of the function and 2 or 0 or t is the value at which to evaluate the function.
If I say, what is 2(x+1) or x(2y + 7x), then the context is obviously multiplication.
With more time, it will become second nature!
AND - there are some other meanings of ( ) as well!
Keep Studying!
• hi this is from 2022 im 13 :D
• its 2023 and im 15
• What if the rate of change was not constant? How much harder would this become? I bet this is the advent of calculus?
• Nice question!

Yes, you are correct that functions with non-constant rates of change are the advent of calculus! For example, suppose we are given the ice sheet's initial thickness and also given the rate of change of the thickness as a function of time. To find the formula for the thickness as a function of time, we would need to 1) find the anti-derivative of the rate of change function, then 2) use the initial thickness to solve for the constant term that appears in the anti-derivative. (Derivatives and anti-derivatives are the two main operations in calculus, and both operations are ultimately based on the concept of a limit.)

Have a blessed, wonderful day!
• can you do this in the form Y=mx+b?
• At about @ in the video, Sal shows you that he is using y=mx+b, but the the variables are swapped to different letters to match the ones used in the problem description.
• At what exactly does denote mean in math terms?
• It basically just means "represent." Sal is saying that S(t) means "the thickness of the ice (represented by S) as a function of time (represented by t)."
• Why did Sal use the slope-intercept form to find the equation for this question?
• Good question. We need to use the slope-intercept form, because we are asked to create an equation. While creating an equation, we use this form so that we get the x and y-intercept, which serves as the constant rate to our answer.
For example, let's say that you bought 7 apples each month, and you already had 4 apples at home. You're asked to create its equation.(I know this is a terrible question) How will you do that? Well, we can use the slope-intercept form to figure it out!
The constant rate will be 7, since you bought 7 apples each month. How will we create an equation out of it? Simple.
y = mx+b
y =(the constant rate)x+(what we started out with, or b)
y= 7x+4
Didn't use a great vocabulary, but hope this helps!!
• So what's the difference between a graph and t-chart?
• A graph is a coordinate plane that expresses data using a line, points, etc. On the other hand, a t-chart uses only numbers, or words, to express data. The t-chart is not very visual, while the graph is.
• If slope means depth, then I'm out of my slope here.
• At , Sal's equation is S(t) = -0.25t +2. Is S(t) the dependent variable or just S?
• S(t) is a function not a dependent variable.
A function is kind of a box which takes a number and throws a different number back.
The name of the box is S and the number you put in is t ( which could be any number ).
Let us say that t is 4 and we throw 4 in the S box, inside the box, we multiply 4 * -0.25 which equals -1 , then we add 2 to it.
If we see it in the equation form it will look like this:
S(4) = -0.25 * (4) + 2