Question

Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the copier, the copy is reduced by 12%. What formula shows the pattern for the size of each copy of the photograph as it is reduced? What is the length of the photograph’s copy if Timothy presses the reduce button 5 times? Round to the nearest tenth.

Answer 1

Answer:

length of the photograph will be 4.2 in. after pressing the button 5 times.

Step-by-step explanation:

By pressing the button, every time size of the photograph gets reduced by 12%.

Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,

L = $l(1-\frac{12}{100})^{n}$

Where l = Actual length of the photograph

L = length of the reduced image

n = Number of times the button has been pressed

For l = 8 in. and n = 5

L = $8(1-0.12)^{5}$

  = $8(0.88)^{5}$

  = 4.22 in

L ≈ 4.2 in.

Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.