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grigory [225]
3 years ago
8

Help meeeee plssss!!!!!!!!

Mathematics
1 answer:
Svetllana [295]3 years ago
6 0
The slope is -3/4 :)
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A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.
tatyana61 [14]

Answer:

(a)g(n)=0.05\cdot 2^n

(b)g^{-1}(n)=\log_{2}20g(n)

(c)43 times

Step-by-step explanation:

<u>Part A</u>

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n

<u>Part B</u>

<u />g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)<u />

<u />

<u>Part C</u>

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

3 0
3 years ago
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