Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
7. Modeling with Exponential and Logarithmic Functions
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Exercise 25 Page 347

We will first create a table of data pairs using the given information.

Age (in years),
Near point (in centimeters),

Next, we will plot the transformed points.

The points lie close to a line, so an exponential model should be a good fit for the original data. To write an exponential model let's use the points and because they appear to be on the line. With this, we will write an equation in point-slope form.
In this form, is the slope and is a reference point that is on the line. Using the Slope Formula, we can substitute the chosen points and find the slope.
Now that we found the slope, we can write the equation in point-slope form. Let the point be our reference point.
Next, we will isolate to have the model in the form of
Solve for

As a result, one possible model is depending on the choice of the points.