What is the purpose of the folded inner membrane in mitochondria

Increase the membrane surface area which creates more work space

Explanation:

Mitochondrion (Plural-mitochondria) is referred to as the powerhouse the the cell because it is the site of ATP (energy rich compound) synthesis in the cell. Mitochondria are shaped perfectly to maximize their productivity. They are made of two membranes; the outer membrane, which sheds the organnelle and contains it like a skin and the inner membrane, which folds over many times and creates a layered invagination called CRISTAE.

The folding of the inner membrane increases the membrane surface area inside the organnelle. Since many of the chemical reactions e.g. Cellular respiration (ETC and Chemiosmosis) occur in the inner membrane, the increased surface area creates more space for the reactions to occur.

It is just reasonable that the more the space, the more the work that can be done.

this would be a math

multiply it by 5 in order for you to understand i cant give an exact answer.