Postage rates Assume postage for sending a first-class letter ...

Question

Postage rates Assume postage for sending a first-class letter in the United States is $0.47 for the first ounce (up to and including 1 oz) plus $0.21 for each additional ounce (up to and including each additional ounce).

a. Graph the function p=f(w) that gives the postage p for sending a letter that weighs w ounces, for 0<w≤3.5.

a. Graph the function p=f(w) that gives the postage p for sending a letter that weighs w ounces, for 0

Accepted Answer

Welcome back, everyone. In this problem, a local bakery sells sourdough bread for $3 for the first pound and 75 cents for each additional pound. Graph the function P equals FFW that gives the cost for selling sourdough bread that weighs 2 pounds for W between 0 and 2.5. And here we have a graph that we can use to plot P equals FFW. Now this part of our problem P equals F of W. What it basically tells us is that our price is a function of how much pounds of sourdough bread is sold, and in our problem statement we have two conditions. First, we know that the bread is sold for $3 for the first pound. And then we know it's sold for 75 cents for each additional pound. So we know that our graph is going to be linear, but the way our function looks will depend on how much pounds of sourdough bread is sold. So let's break down both of these conditions to get an equation for both times, I mean before the first pound and after the 1 pound, and then we can plot it on our graph by finding some points for each, uh, each part of our function. Now let's start with the first scenario. The bread is sold for $3 for the first pound, OK? So what does this tell us? Well, this tells us then that for W being less than or equal to 1, OK, let me put this in red here. Then P is going to be equal to 3, OK? It doesn't matter what happens, we know it's going to be sold for $3 for the first pound. Now, that means then that on our graph, when we have our value of W here, that is our horizontal axis. Let's put W here and let's put P here. So this is P and W. OK. Then that means. That From W starting at 0 to 1, not including 0, P will be equal to 3. So we can draw a straight line here. Let me put it in red. OK, can draw a straight line here and we know that when W is 0, that's gonna be empty. It's not a part of the function. And then when W equals 1, this, this point is going to be filled, including when W equals 1. Now what about the next part of our problem? It's 75 cents for each additional pound. Well, no, that means. For greater than 1, OK. Then P Is going to be equal to 3 + 0.75 multiplied by W minus 1, OK? Because think about it. When we take away one from whatever pound this is, that would account for our $3 here that we initially started with, right? So, no, that means we can go ahead. We already know one of the points. We know it starts at, uh, it starts at the point where WE equals 1, but if we can find another point, then we can plot our graph for W greater than 1. So what is our graph going to be? Well, when W equals 2, for example. Then P W P 2 is going to be equal to 3 + 0.75 multiplied by 2 minus 12 minus 1 is 1, and 3 + 0.75 equals 3.75. Thus, when W equals 2, P is $3.75. So if we go to our graph, when W equals 2, this is gonna be 3.75, which is gonna be right here. OK, that's gonna be a point. And we also know that our graph stops when W equals 2.5. So it's gonna stop, the cut-off point is gonna be along this line here, OK? So now that we know that, let's go ahead and plot our graph. Starting here, going all the way through. And now, as we said, we know that it's going to stop when WE calls 2.5. So it's gonna start right here, OK. And it's also going to include that point because remember in our domain, we were told that double was between 0 and 2.5. Therefore, this is going to be the graph of P equals F of W for our baker problem. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Piecewise Functions

Graphing Functions

Linear Functions

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