Begin by creating a table of data pairs (x,ln y) using the given information.
Possible Model: y=2.48(1.06)^x
Practice makes perfect
We will first create a table of data pairs (x,ln y) using the given information.
Age (in years), x
20
30
40
50
60
Near point (in centimeters), y
12
15
25
40
100
ln y
2.48
2.71
3.22
3.69
4.61
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 y=ab^x, let's use the points ( 30, 2.71) and ( 60, 4.61) because they appear to be on the line. With this, we will write an equation in point-slope form.
ln y- ln y_1= m(x- x_1)
In this form, m is the slope and ( x_1, ln y_1) 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 ( 30, 2.71) be our reference point.
ln y-2.71=0.06(x-30)
Next, we will isolate y to have the model in the form of y=ab^x.
