Question

Can y’all help with this? Thanks

Answer 1

Answers:  

Exponential decay model is y = 500*0.88^x

There is roughly 0.0000000000237 mL of the original air left.

There are 10 zeros between the decimal point and the '2'

The number in scientific notation is $0.0000000000237 = 2.37 \times 10^{-11}$

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Further Explanation:

A general exponential equation is

y = a*b^x

We start with 500 mL of air which is the value of 'a'

If 12% of the air is replaced, then 88% of it remains because 12% + 88% = 100%

Convert 88% to the decimal form 0.88 and this represents the base of the exponent. This is the value of b.

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Since a = 500 and b = 0.88, we have

y = a*b^x

y = 500*0.88^x

Now we plug in x = 240 to estimate how much of the original air is in the lungs after that many breaths.

y = 500*0.88^x

y = 500*0.88^240

y = 0.0000000000237

This number is very small and to be expected since quite a bit of breaths have occurred. Nearly all of the original air particles should be replaced by this point. A very small trace amount remains.

Notes:

• There are 10 zeros between the decimal point and the '2' in the number 0.0000000000237
• The number 0.0000000000237 is so small that it probably makes sense to use scientific notation to write $0.0000000000237 = 2.37 \times 10^{-11}$ meaning we move the decimal point 11 spots to the left to go from 2.37 back to 0.0000000000237
• The number 0.0000000000237 is read out as "237 ten-trillionths". Imagine splitting an object into ten trillion tiny pieces, and then shading 237 of those pieces to represent this decimal number.