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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)

User Johnrechd
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1 Answer

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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

User GsMalhotra
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