Explanation:
a. The thickness of a piece of paper increases each time it is folded. When the paper is folded in half, the thickness doubles because the two layers are now stacked on top of each other. If the paper is folded again, the thickness doubles again because there are now four layers. As the number of folds increases, the number of layers and the overall thickness of the paper increases exponentially. Therefore, the thickness in inches, t, is a function of the number of times the paper is folded, n.
b. We can represent the relationship between t and n using the function:
f(n) = 0.004 x 2^n
This function takes the number of folds, n, as input and outputs the corresponding thickness, t, in inches. Each time the paper is folded, the thickness is multiplied by 2, so we raise 2 to the power of n. The initial thickness of the paper is 0.004 inches, so we multiply this by 2^n to get the total thickness after n folds. Therefore, the function f(n) = 0.004 x 2^n represents the relationship between t and n.