Problem

In Exercises $1-10$ , match the numerical model t…

05:39

Problem 8 Medium Difficulty

In Exercises $1-10$ , match the numerical model to the corresponding graphical model $(a-j)$ and algebraic model $(k-t) .$
$$
\begin{array}{|c|c|c|c|c|c|c|}\hline x & {4} & {8} & {12} & {14} & {18} & {24} \\ \hline y & {20} & {72} & {156} & {210} & {342} & {600} \\ \hline\end{array}
$$

Answer

Algebraic model: (k)
Graphical model: (j)

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Video Transcript

So in this problem, we're given this numerical model here by this table of numbers and were asked to determine the graphical model from the graphs that are given and the algebraic model from the models that are given. All right. So, let's let's just try something here for a second. Let's try algebraic model K. Which says that why equals X squared plus X. Mm. So interesting When X is four and we have Y equal to four squared plus four, which is 16 plus four is 20. And that matches our table, doesn't it? All right, Let's do another 1. 1 4 is eight. I'm sorry. When X is eight then why is eight squared plus eight? Well, he's square. It is 64. Let's eight. That's 72. Mm. Cool, that matches as well. All right. So, what happens when X is 12? Why is 12 squared plus 12? 12 squared? That's 144 plus 12. That's 1:56. Look at that that matched as well. Well, what happens when X is 14 then? Why is 14 squared plus 14? Well, let's see. 14 squared is how much? 1 96 Plus 14 would be To 10, wouldn't it? And that matches. Okay, So what happens when X is 18? Why is 18 squared plus 18? So 18 squared is 3 24 plus another 18 Would be 3 42, isn't it? Okay, so that checks. One last point to check x equals 24 Then why is 24 squared plus 24? Which is what we'll 24 squared Is 5 76 plus 24. That's 600. And that checks. So every point it was verified, we immediately now know that that is the algebraic model. So now the question is which is the graphical model that matches this? Well, let's go right to our graphing calculator for a second and do why equals X. Word plus X. And there's the graph that we get right there. So which one of those graphs is that? Well, we look really close. We can see that model. J does the same grab right? It's just drawn drum like this, that's how it's done. What's done like I'm like that. Okay, Anyway, you get the idea, it's like that. So this graphical model jane.

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