Question

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)

Answer 1

Answer: 1)
`t(n)=0.6(2)^n`

2)
`f(x)=10(5)^x`

Explanation:

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

`t(n) = ab^n` ---------(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),

`0.6 = a(b)^0\implies 0.6 = a`

Hence the function that shows the given situation,

`t(n) = 0.6 b^n` -----------(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),

`1.2 = 0.6 b^1\implies 2 = b`

Thus, the complete function is,

`t(n) = 0.6 (2)^n`

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

`f(x) = ab^x` ---------(1)

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

By equation (1),

`2= ab^(-1)` ---------(2)

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

Again, By equation (1),

`(2)/(5)= a(b)^(-2)`

`\implies (2)/(5)=ab^(-1)b^(-1)=2b^(-1)`

`\implies (2)/(5)=(2)/(b)`

`\implies 2b=10`

`\implies b = 5`

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),

`f(x) = 10(5)^x`