Chapter 4.3, Problem 5E

Reminder Round all answers to two decimal places unless otherwise indicated.

Making Guitars As a luthicr, you make high-rituality guitars for which accurate fret placement is crucial. Referring to Figure 4.18, we think of the nut itself as fret 0. Additional frets are numbered as we move from the nut toward the saddle.

The following table shows the distance $D\left(n\right)$, in inches, from the saddle to the $n\text{th}$ fret.

$n=\text{fret}\text{number}$	$\begin{array}{l}D=\text{distance}\text{to}\\ \text{saddle,}\text{in}\text{inches}\end{array}$
$0$	$25.00$
$1$	$23.60$
$2$	$22.27$
$3$	$21.02$
$4$	$19.84$

a. Show that the data are exponential.

b. Make an exponential model that shows the distance from the nth fret to the saddle.

c. According to your model, how far is it from the fifth fret to the sixth fret?