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Minchanka [31]
3 years ago
8

Does anybody know how to do time with exponential decay

Mathematics
1 answer:
My name is Ann [436]3 years ago
5 0
<span>From the message you sent me:

when you breathe normally, about 12 % of the air of your lungs is replaced with each breath. how much of the original 500 ml remains after 50 breaths

If you think of number of breaths that you take as a time measurement, you can model the amount of air from the first breath you take left in your lungs with the recursive function

b_n=0.12\times b_{n-1}

Why does this work? Initially, you start with 500 mL of air that you breathe in, so b_1=500\text{ mL}. After the second breath, you have 12% of the original air left in your lungs, or b_2=0.12\timesb_1=0.12\times500=60\text{ mL}. After the third breath, you have b_3=0.12\timesb_2=0.12\times60=7.2\text{ mL}, and so on.

You can find the amount of original air left in your lungs after n breaths by solving for b_n explicitly. This isn't too hard:

b_n=0.12b_{n-1}=0.12(0.12b_{n-2})=0.12^2b_{n-2}=0.12(0.12b_{n-3})=0.12^3b_{n-3}=\cdots

and so on. The pattern is such that you arrive at

b_n=0.12^{n-1}b_1

and so the amount of air remaining after 50 breaths is

b_{50}=0.12^{50-1}b_1=0.12^{49}\times500\approx3.7918\times10^{-43}

which is a very small number close to zero.</span>
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Another thing is to multiply 59 by 8, which will give you 472. Now we add 472 and 236 and we get 708.

59 x 8 = 472 + 236 = 708.

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3 years ago
Read 2 more answers
Part C: Find the distance from B to E and from P to E. Show your work. (4 points)
My name is Ann [436]

Answer:

Part 1) BE=266\frac{2}{3}\ ft

Part 2) PE=233\frac{1}{3}\ ft

Step-by-step explanation:

Part  1)

<u><em>Find the distance from B to E</em></u>

To solve this problem I assume that CGRP is a parallelogram

so

Triangles CGB and PEB are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

\frac{BG}{BE}=\frac{CB}{PB}

substitute the values

\frac{400}{BE}=\frac{300}{200}

solve for BE

BE=400(200)/300

BE=\frac{800}{3}\ ft

Convert to mixed number

BE=\frac{800}{3}\ ft=\frac{798}{3}+\frac{2}{3}=266\frac{2}{3}\ ft

Part 2)

<u><em>Find the distance from P to E</em></u>

\frac{CG}{PE}=\frac{CB}{PB}

substitute the values

\frac{350}{PE}=\frac{300}{200}

solve for PE

PE=350(200)/300

PE=\frac{700}{3}\ ft

Convert to mixed number

PE=\frac{700}{3}\ ft=\frac{699}{3}+\frac{1}{3}=233\frac{1}{3}\ ft

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Answer:

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