INSTRUCTOR: OK. In this question, we have some xy data. And we're told the data can be modeled by a logarithmic regression function of this form. So we're going to use Desmos log regression functions to find the equation that best fits the data and equation of this form. So I'm going to first take my data. I want to get this over here into Desmos in a table. As we know, we can either manually type it in-- that can be a little tedious. Or usually, we can copy and paste the data in. 

So I'm going to select the data, not the header rows, just the data values. And I'm going to copy that to my clipboard, either with a right-click or Control-C. And then I'm going to come over here and I'm going to paste it in with Control-V. Notice it automatically zoom fits my data. So here's the data as a scatter plot. And I want to now use the built-in Desmos regression tools to find the curve of this form that best models the data. 

So I'm going to click on the regression tools. And it's going to default to a linear regression model. But we are specifically told we want a logarithmic regression function of this form, a plus times natural log of x. So I'm going to go down here in the options under the dropdown menu and pick Logarithmic Regression. And I'm going to select Log Mode. So we always do log mode in Desmos when we do either an exponential or a logarithmic regression. 

And now we can see the curve over here that best fits the data. And we can see the logarithmic model here under the equation. If you want to just verify exactly what the regression model is, you can always click on the three dot menu. And you can verify, for example, exactly what the regression structure is-- a plus b times ln x. That's exactly what we want. And we can see the model here. 

So we want to round the values of a and b to the nearest tenth and enter that as our logarithmic regression function. Now, in the next part of the problem, it says, according to the logarithmic regression function, determine the y for x equal 195 and round to one decimal place. So this is just simply asking us to find the value of y on the regression function. What value does y take on when x equals 195? 

So that just means we're going to evaluate our regression equation for the value x equal 195. There's a really easy way to do this right here in Desmos. I'm going to hover over this icon by equation and export the equation into the calculator list. And then I just replace the x here with the value 195. And that gives me the y value on this curve when x equals 195. So I'm going to round that to one decimal place and enter that as my answer here.