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.

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 = [tex]l(1-\frac{12}{100})^{n}[/tex]

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 = [tex]8(1-0.12)^{5}[/tex]

= [tex]8(0.88)^{5}[/tex]

= 4.22 in

L ≈ 4.2 in.

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

MrRoyal MrRoyal · Answer 2 · 2022-01-25T12:25:44+01:00

The length of the photograph's copy when the button is pressed the 5th times is 4.2 inches

The question is an illustration of an exponential function.

An exponential function is represented as:

[tex]y = ab^x[/tex]

Where:

a represents the initial value i.e. a = 8
b = 1 - r; and r represents the rate. i.e. r = 12%.

So, the function becomes

[tex]y = 8 \times (1 - 12\%)^x[/tex]

Express 12% as decimal

[tex]y = 8 \times (1 - 0.12)^x[/tex]

This gives

[tex]y = 8 \times 0.88^x[/tex]

When the button is pressed the 5th times, we have:

[tex]y = 8 \times 0.88^5[/tex]

[tex]y = 4.2[/tex]

Hence, the length of the photograph's copy is 4.2 inches

Read more about exponential functions at:

https://brainly.com/question/11464095