Solved on Feb 13, 2024

Exposure time to reach coma-inducing CO level: T=.0002x2.316x+127.9T=.0002 x^{2}-.316 x+127.9, where xx is CO in ppm. Find exposure time when x=560x=560 ppm. Round to nearest tenth.

STEP 1

Assumptions
1. The quadratic model for exposure time is T=.0002x2.316x+127.9T=.0002x^{2}-.316x+127.9.
2. The variable TT represents the exposure time in hours.
3. The variable xx represents the concentration of carbon monoxide in parts per million (ppm).
4. The value of xx is within the range 500x800500 \leq x \leq 800.
5. We are asked to find the exposure time when x=560x=560.

STEP 2

To find the exposure time for x=560x=560, we substitute x=560x=560 into the quadratic model.
T=.0002x2.316x+127.9T=.0002x^{2}-.316x+127.9

STEP 3

Substitute x=560x=560 into the equation.
T=.0002(560)2.316(560)+127.9T=.0002(560)^{2}-.316(560)+127.9

STEP 4

Calculate the square of 560.
(560)2=313600(560)^{2} = 313600

STEP 5

Multiply the result by .0002.0002.
T=.0002313600T=.0002 \cdot 313600

STEP 6

Calculate the product.
T=62.72T=62.72

STEP 7

Now, calculate the product of .316.316 and 560560.
T=.316560T=-.316 \cdot 560

STEP 8

Calculate the product.
T=176.96T=-176.96

STEP 9

Combine all the terms to find the value of TT.
T=62.72176.96+127.9T=62.72 - 176.96 + 127.9

STEP 10

Calculate the sum.
T=62.72176.96+127.9=13.66T=62.72 - 176.96 + 127.9 = 13.66

STEP 11

Round the result to the nearest tenth as needed.
T13.7 hoursT \approx 13.7 \text{ hours}
The exposure time when x=560x=560 is approximately 13.7 hours.

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