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(a) Find the logarithmic regression function that best fits the following data set: (2,0.71),(3,1.07),(4,1.41),(5,1.65),(6,1.82) . (b) Using the regression equation, what are the $y$ -coordinates when $x=1$ and $x=8 ?$

(a) $-0.023609+1.030215 \ln x$(b) -0.023609,2.11866

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 5

Logarithmic Functions

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Harvey Mudd College

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this question has given us uh five data points you can see, I'm listed at the top right here. And what we wanna do is first find the logarithmic regression function. Which best models the data. So you can see bubbled in on the right hand side. The directions to do this on A. T. I. 84 plus calculator. So if you go ahead and follow those steps what you'll end up getting the calculator will produce it for you. It's pretty straightforward. You'll get a log arrhythmic regression function which is going to be in the form why is equal to a plus B. L. N. X. And it's going to produce for you these values for A. And B. And what you'll end up seeing is that this algorithm log arrhythmic regression function. Best modeling the data is why is equal to -0.02369 plus 1.030-15 L. N. X. Now part B. Here just wants us to find why when X. Is equal to one and when X is equal to eight. And we're just going to use this logarithmic regression function we just found in part A. So all we need to do is plug in these different values for X. So plug in X equals one into our regression function and then plug in X equals eight into our regression function. And again fairly straightforward. You just plug it into your calculator. And what we get for part B is when X is equal to one We have y. is equal to negative 0.023 69. And when Y when X is equal to eight, we have Y is equal to 2.11866.

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