Using Models Use the model given to answer the questions about the object or process being modeled.

An ocean diver models the pressure $P$ ( in $\mathrm{lb} / \mathrm{in}^{2} )$ )
at depth $d$ (in ft) by

$$P=14.7+0.45 d$$

(a) Make a table that gives the pressure for each 10 -ft
change in depth, from a depth of 0 ft to 60 $\mathrm{ft}$ .
(b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth?

Answer

a)
Pressure $\mathrm{P}\left(\mathrm{lb} / \mathrm{in}^{2}\right)$ 14.7$\quad 19.2 \quad 23.7 \quad 28.2 \quad 32.7 \quad 37.2 \quad 41.7$
depth d (ft) 0$\quad 10 \quad 20 \quad 30 \quad 40 \quad 50 \quad 60$
b)
$30=12.7+0.45 d$
$0.45 d=17.3$
$d \approx 38.44 \mathrm{ft}$

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Modeling the Real World with Algebra

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Video Transcript

All right. So the first question is asking a makeup table when there's a changing death from zero fee to 60 feet and we just have to find a pressure. So the question is, P equals 14.7 plus 0.45 D. And while pieces for the pressure and pounds per inch six inch square, the descends for feet. So what we're gonna do is we're gonna plug ins, er, first Indy. So pressure the coast of 14.7 plus 0.45 times zero. Then we're gonna get 14.70 equals to zero. And we guys just say P one for that one pressure, too. And when I say 14.7, close 0.45 times 10 Because, uh, you have to realize that tea and the they are the variable. So there go one the changing it while the 14.7 and 0.45 of the constants. So they are the constant, even though when the pressure and death still changes. And if you have more questions about those kind of constant, you can refer to page 1 60 on chapter one, Section 10. I can't look this screen shot for you are there. So it says that whenever the Kate Kate like was K X and Katie's not zero, then we says it's a direct variation, So let's get going so t to you close to for 10 points. Seven. Close point 4.5 and that will be equal to what you playing the calculator. You'll get 19.2 O P. Three keep on point for five times 20. This time there will be 14.7 plus nine and then equal to 20 points 23.7. Crusher four equals to 14.7 plus 0.45 times 30. That will be equal to 13.5. And if you put in, the calculator will be 28 point, and you just kept going until we reach to 60. So why not do the rest of them? And you realize that there's a pattern starting to show up? Oh, actually, this is 47. I made a mistake, Uh, each 10 minute interval. It's increasing by a 4.5. As you can tell, they will be 45 times 40 Shelby's that lies 18 3.7 P six equals to 14.7 plus fire times 60 50 that is equal to I'll put in calculator 37.2 and lastly for pressure 7 14.7 Close 1445 times 60. We're gonna stop at 60 and that will be equal to a close 27. And once you put in the calculator well before you want to be seven and just want to make sure that we have to put all of those inches Sorry, pilots were inches square for all this. That So that's the first question and all we have to do. Just make a table. Oh, don't have a good tensile to draw this. Basically, this the will stands for deaf and people sense for a pee and the silver zero. Hey, 20 30 40 50 and 60. Ah, so this will dispel. You'll BP one p to p. Three p. Four p. Five p six Piece of values This'll only 14.7 19.233 point 7 28.2 33.7 37.2 and 41.7 and you can just write, uh, unit here and that unit waas feet And here it was pound per inch squared. So that's the first question, basically uses it plugging in uh, and the Rite Valu and for Let her be. It's asking now if the pressure is 30 pounds per square, what's going to death? So their friends between first question, the second question is that the first question they gave you Beth Value and you have to find a pressure. And now they give the pressure and we have to fund death. So all we have to do is, yeah, credit text here. So pressure here, of course, the 30 and that will be equals to 14.7 plus point for five times the. And we're gonna just stay here and just keep the d because we don't know what's gonna be variable yet. And we're trying to find the answer. So 30 minus 14.7, that's it. Call to 15.3, and that's it's also equal to point for five and the will be equals to 15.3, divided by 0.5. And if you actually plug and put that into calculator, you'll have 34 and you know it will be what All right, thank you.

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