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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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9. Water is added to two containers for 16 minutes. The equations below model the ounces of
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The two containers hold 328 ounces at the they hold same amount of water.

<u>Step-by-step explanation:</u>

The equations below model the ounces of  water, y, in each container after x minutes.

y = 16x + 104

y = -2x^{2} +40x+160

At the time after the start when the containers hold  the same amount of water, the two equations must be equal.

⇒ 16 x + 104 = -2x^{2}  + 40 x + 160

The first step is to divide everything by 2 to make it simplified.

⇒ 8 x + 52 = - x^2 +20 x + 80

Now put everything on the left .

x^2 + 8 x - 20 x + 52 - 80 = 0

Add the like terms together to further reduce the equation

x^2 - 12 x - 28 = 0

Factorizing the equation to find the roots of the equation.

Here, b = -12 and c = -28

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Take x = 14  and substitute in any of the given two equations,

⇒ y = 16(14) + 104

⇒ y =224+104

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∴ The two containers hold 328 ounces at the they hold same amount of water.

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3 years ago
I need some help
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<span>The best answer to this problem is 0.0823. np = 48 * 1/4 = 12 The exactly 15 would be written as 14.5 to 15.5. You then plug those into you equation separately. e1= (14.5-12)/3 = 0.833 and e2 =(15.5 - 12)/3 = 1.167) p(0.833<e<1.167)= 0.0808</span>
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