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 1.5 grams. Six minutes since the experiment started, the remaining gas had a mass of 60 grams. Let I 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. 35 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
Let
t -----> number of minutes
y ----> the mass in grams
we have that
m=-1.5 g/min ----> is negative because is a decreasing function
point (6,60)
Find the equation of the line in slope intercept form
y=mt+b
we have
m=-1.5
point (6,60)
substitute
60=-1.5(6)+b
solve for b
60=-9+b
b=60+9
b=69
the linear equation is
y=-1.5t+69
Part b
For t=35 min
substitute
y=-1.5(35)+69
y=16.5 grams
Part c
For y=0
substitute
0=-1.5t+69
1.5t=69
t=46 minutes