Chapter 7.8, Problem 33P

Suppose you want to make a reduced copy of a photograph that has an actual length of 8 inches. Each time you press the reduce button on the copier, the copy is reduced by $12\%.$

What is the length of the photograph’s copy if you press the reduce button 5 times? Round to the nearest hundredth.

To determine

To find : the length of the photograph’s copy if the reduce button is pressed 5 times.

Answer to Problem 33P

4.22 inches

Explanation of Solution

Given information: Suppose we want to make a reduced copy of photograph that has an actual length of 8 inches. Each time we press the reduce button on the copier, the copy is reduced by 12 %.

Simplification:

Let $a_0$ represents the original length of the photograph and $a_n$ is the length of the photograph after pressing the reduce button n times.

Then the sequence $a_0,a_1,a_2,a_3,a_4,\mathrm{.....}$ is geometric sequence with first term $a_0=8$ and common ratio, $r=0.88$ .

Length of the photograph after pressing the reduce button 5 times is

  $\begin{array}{l}{a}_5=a_0{r}^5\\ a_5=8{\left(0.88\right)}^5=4.22\text{inch}\end{array}$

Length of the photograph after pressing the reduce button 5 times is 4.22 inches.