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. Each minute, they lose 2.8 grams. Seven minutes since the experiment started, the remaining gas had a mass of 106.4 grams. Let 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) 37 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

The form of the linear equation is y = mx + b, where

m is the rate of change (slope the line)

b is the initial amount (y-intercept)

The gas has leaked at a rate of -2.8 gram per minute

Then m = -2.8

Let y is the mass of gas in x minutes, then

y = -2.8x + b

To find b, we need a point on the line

Since in 7 minutes, the remaining of the gas is 106.4

That means the point is (7, 106.4)

Substitute it in the equation to find b

106.4 = -2.8(7) + b

106.4 = -19.6 + b

Add 19.6 to both sides

106.4 + 19.6 = -19.6 + 19.6 + b

126 = b

The equation is

A) y = -2.8x + 126

Since x = 37 min

Substitute it in the equation to find y

y = -2.8(37) + 126

y = 22.4 grams

B) The gas left after 37 min is 22.4 grams

All gas will be gone means y = 0

Then substitute y by 0

0 = -2.8x + 126

Add 2.8x to both sides

0+2.8x = -2.8x - 2.8x + 126

2.8x = 126

Divide both sides by 2.8

x = 45

C) The gas will be one after 45 minutes