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Find an exponential function determined by the data in Table 8 .$$\begin{array}{|l|l|l|l|}\hline 20 & 40 & 60 & 80 \\\hline 100 & 72 & 51.84 & 37.3258 \\\hline\end{array}$$

$$138.887(0.72)^{x / 20} \approx 138.887(0.983709)^{x}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Missouri State University

Campbell University

McMaster University

Lectures

02:51

Find an exponential functi…

02:45

00:39

Find exponential functions…

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01:01

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For the following exercise…

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Enter the data from each t…

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So if we want to find an exponential equation that represents this function here for this data, um, I would assume depending on which point you pick, you might get something slightly different. But I'm just going to go ahead and choose the first two. Um, And if you're doing this and you choose different points and you get something different, it's just because of the points you chose. Not necessarily. Because you may have done something wrong. Um, yeah, So I'm not really going to check those. I'm just going to use these first two and then kind of go from there. So we're gonna start with the equation. Why is it to a to the V X and we're going to plug these in and we'll get a system and then we can solve that system. So, um, if I plug in 20 I should get output of 100 so it would be 100 is equal to a B to 20 and then when we plug into 40 we should get out 72. So it would be a B to the 40 now. We could go ahead and solve for a, um and then just set them equal. But what I'm going to do is just divide each of these equations because knows if we divide them, the A's will cancel out. So we'll have 72 over 100. Ah, which would just give us, um, 0.72 mhm. And then over here, the A's cancel and then be to the 40 over beat 20. No, we subtract the powers that just gives us be to the 20. Now we can go ahead and take the one over 20th power on each side. They cancel out on the right, and then we just get B is equal to 0.72 raised to the one over 20th power. Now to figure out what a is, we could just take this, plug it into one of the equations we got before I plug it into the second one. So the 100 is equal to a time 0.12 ready to the one over 20th raised to the 20th that was cancelled. And then we can just divide by 0.7 to do I say one. I don't know what I was writing. I guess I can't read my own handwriting. Well, seven two. So now we divide that over. So 100 divided by 1000.72 Uh, that would give us upside. Just kind of repeats on. So would be 1250 over nine is gray, right? And now we can go ahead and plug everything into our original question Would be, Why is it to 1250 over nine and then we'd have 0.72 raise the one of the 20th race to the X, and then we can go ahead and distribute that power of X, multiply the powers, and that would give us 0.72 raised to the X over 20. And this is just one possible exponential. Because again, like I said, if you get something slightly different than what I have here, then it may just because you use two different points. Um, and that doesn't necessarily mean, um, to answer you got was wrong, but, um I mean, hopefully the rest of the data gives us the same equation.

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