1. writing an equation for an exponential function by 2. a piece of paper that is 0.6 millimeter thick is folded. write an equation for the thickness t of the paper in millimeters as a function of the number n of folds. the equation is t(n)= 3. enter an equation for the function that includes the points. (-2, 2/5) and (-1,2)

1)

2)

Step-by-step explanation:

1) Let the function that shows the thickness of the paper after n folds,

        ---------(1)

Since, According to the question,

Initially the thickness of the paper = 0.6

That is, at n = 0, t(0) = 0.6

By equation (1),

Hence the function that shows the given situation,

      -----------(2)

Again when we fold the paper the thickness of the paper will be doubled.

Thus, at n = 1, t(1) = 1.2

By equation (2),

Thus, the complete function is,

2) Let the function that is passing through the points (-2, 2/5) and (-1,2),

        ---------(1)

For f(x) = 2, x = -1

By equation (1),

      ---------(2)

Also, For f(x) = 2/5, x = -2

Again, By equation (1),

By substituting this value in equation (2),

We get, a = 10

Hence, from equation (1), the function that is passing through the points (-2, 2/5) and (-1,2),