Chantel drew a picture of her dog on a piece of paper that is 12 centimeters long. She used a copy machine to enlarge her drawing. She used the 115% setting to make each new copy. She then used each new copy, using the same copier setting. Enter an explicit and recursive formula that will give the length of the new copy.

an=
an= ;=12

To find an explicit formula for the length of each new copy, we can use the concept of compound interest. The length of each new copy is increasing by 15% (115% - 100%) each time.

Let's denote the length of the original drawing as L, which is 12 centimeters in this case.

The explicit formula to find the length of the nth new copy (an) can be expressed as:

an = L * (1 + r)^n

where L is the initial length (12 centimeters), r is the growth rate (15% or 0.15), and n is the number of copies.

Therefore, the explicit formula for the length of each new copy is:

an = 12 * (1 + 0.15)^n

For example:
- The length of the 1st new copy (n=1):
a1 = 12 * (1 + 0.15)^1 = 12 * 1.15 = 13.8 centimeters

- The length of the 2nd new copy (n=2):
a2 = 12 * (1 + 0.15)^2 = 12 * 1.3225 = 15.87 centimeters

And so on...

To find the recursive formula for the length of each new copy, we can use the fact that each new copy is obtained by multiplying the previous copy by the growth rate (r = 0.15).

Let's denote the length of the nth new copy as an and the length of the (n-1)th new copy as an-1.

The recursive formula for the length of each new copy is:

an = an-1 * (1 + r)

In this case:

a1 = L * (1 + r)
= 12 * (1 + 0.15)
= 12 * 1.15
= 13.8 centimeters

a2 = a1 * (1 + r)
= 13.8 * (1 + 0.15)
= 13.8 * 1.15
= 15.87 centimeters

And so on...

The explicit formula for the length of the new copy, denoted by an, is:

an = 12 * 1.15^n

The recursive formula for the length of the new copy, denoted by an, is:

a1 = 12
an+1 = an * 1.15

An= 1.15(n-1)