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Find an exponential function determined by the data in Table 6$$\begin{array}{|l|l|l|l|}\hline 10 & 20 & 30 & 40 \\\hline 15.7 & 50.24 & 160.768 & 514.458 \\\hline\end{array}$$

$$4.90625(3.2)^{x / 10} \approx 4.90625(1.12335)^{x}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Campbell University

Idaho State University

Lectures

02:45

Find an exponential functi…

03:25

03:05

00:29

Find exponential functions…

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00:39

00:32

00:37

01:01

00:26

00:38

01:06

00:33

00:31

So if we want to try to come up with an exponential function for this data, um, we could just use two of these points, um, to construct this equation, It doesn't really matter which one will be used early site. I don't think it really matters which one we used. We might get something slightly different, depending on which points we pick, but it shouldn't be anything too crazy, um, of a difference. But again, I've not checked the other ones. Um, because I really don't think it matters if we check it. So what I'm gonna do is just use these first two points. So we're going to first use the equation. Why is you get a times beat the X, and then I assume these are, like, the acts of the Y values, and we're going to plug these two points into this equation, and then we'll use that system to help us solve. So what I want to do now, um, I'll plug in 11th. So it be 15.7 is equal to a times B to the 10th, and I wont plug in 20. We should get 50.24 Is it to a B to the 20th. Right now, what I'm going to do is take both of these equations and divide them because dividing them will cancel that a there. So then we would have. So let's see 50.24 divided by 15.7. That gives us 3.2. So we have 3.2 is equal to and then be to the 20 divided by B to the 10th. What? We subtract powers. So be to the 10th and then we can take the 10th power on either side. And then that gives us 3.2 raised to the 1/10. Is it gonna be? And now, in order for us to solve for a, we can just take this and then plug it into one of the equation. So I'm going to plug it into that second one. So would be 15.7 is a and then B is 3.1 to raise to the 1/10 But then that's raised to the 10th. So the tens cancel and then we just need to divide over by 3.2. So we have 15.7 divided by 3.2 and that is equal to 1 57/32. So now we'll go ahead and write out our equations Would be Why is he too? 1 57/32 and then three point to raise to the 1/10 all raised to the X. And you might have got something slightly different from this. Um Then what I did, if you used other points, like I was saying at the start, Um, but at least this is what you would get using the first tube.

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