Answer: To find the number of faces on the last shape produced by the 3-D drawing program, we can start by examining the pattern. The program starts with a 4-faced shape and then continues adding new shapes with 4 times as many faces as the one before.
Let's write down the number of faces for each shape produced:
Shape 1: 4 faces
Shape 2: 4 × 4 = 16 faces
Shape 3: 16 × 4 = 64 faces
We can see that the number of faces doubles each time, which means that the number of faces on the last shape can be found by multiplying the number of faces on the previous shape by 4.
To solve the problem, we can work backwards. Since we know that there were 1,364 faces altogether, we can divide this total by 4 repeatedly until we reach a quotient that is not divisible by 4.
Here's the breakdown:
1,364 ÷ 4 = 341 (Shape 4)
341 ÷ 4 = 85.25 (Shape 3)
85.25 ÷ 4 = 21.3125 (Shape 2)
21.3125 ÷ 4 = 5.328125 (Shape 1)
We stop at Shape 1 because the quotient is not divisible by 4 anymore.
Therefore, the last shape produced by the program had 5 faces.