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 9.7 grams per minute. Eight minutes since the experiment started, the remaining gas had a mass of 339.5 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. 31 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.

Answer 1

Answer: a. This line's slope-intercept equation: y=-9.7x+417.1

b. 31 minutes after the experiment started, there would be 116.4 grams of gas left.

c. If a linear model continues to be accurate,43 minutes since the experiment started, all gas in the container will be gone.

Step-by-step explanation:

Linear equation: y=mx+c  (slope-intercept equation)

, where m= rate of change in y with respect to change in x , c= Initial value.

Let y=   Mass of remaining gas after x minutes.

m= -9.7 (given)

At x= 8, y=339.5

Thus,

$339.5=(-9.7)(8)+c\\\\\Rightarrow\ 339.5=-77.6+c\\\\\Rightarrow\ c= 339.5+77.6=417.1$

a. This line's slope-intercept equation: y=-9.7x+417.1

b. At x= 31 minutes

y=-9.7(31)+417.1

⇒ y=-300.7+417.1

⇒ y=116.4

31 minutes after the experiment started, there would be 116.4 grams of gas left.

c. Put y=0, we get

$0=-9.7x+417.1\\\\ x=\dfrac{417.1}{9.7}\\\\ x=43$

If a linear model continues to be accurate,43 minutes since the experiment started, all gas in the container will be gone.