Scientists are conducting an experiment with a gas in a sealed container. The ma

Question

Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured, and the scientists realize that the gas is leaking over time in a linear way. Its mass is leaking by 6.8 grams per minute. Six minutes since the experiment started, the remaining gas had a mass of 285.6 grams. Let x be the number of minutes that have passed since the experiment started, and let y be the mass of the gas in grams at that moment. Use a linear equation to model the weight of the gas over time. a. This line's slope-intercept equation is. b. 40 minutes after the experiment started, there would be grams of gas left. c. If a linear model continues to be accurate, minutes since the experiment started, all gas in the container will be gone.

Explanation / Answer

Ans(a):

leaking means slope is negative so m=-6.8

then linear equation y=mx+b becomes y=-6.8x+b

after six minute, remaining mass is 285.6

that means at x=6, y=285.6

285.6=-6.8*6+b

285.6=-40.8+b

b=326.4

Hence slope-intercept equation is y=-6.8x+326.4

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Ans(b):

at t=40

y=-6.8x+326.4=-6.8*40+326.4=-272+326.4=54.4

Hence 54.4 grams of gas left

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Ans(c):

all gas gone means y=0

y=-6.8x+326.4

0=-6.8x+326.4

6.8x=326.4

x=48

so answer is 48 minutes.

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