The environment club has saved 200 pounds of cans and promis

The environment club has saved 200 pounds of cans and promises to collect 20 pounds of cans each week and will use the profits to buy additional recycling bins. Construct a linear model for their collection program:

What will the independent variable, x, represent?

What will the dependent,y, represent?

What is the starting value, b, for this model?

What is the slope, m, for this model?

Write the model in y=mx+b form.

How many pounds of cans will the club have by week 12?

When will the club have 320 pounds of cans?

Solution

Let x be the number of weeks from now (after the environment club has collected 200 lbs of cans) and let y be the weight of cans in lbs after x weeks from now. Then, y = 20x + 200... (1) is the linear model for the environment club\'s collection program.

The independent variable x represents the number of weeks after the environment club has collected 200 lbs of cans.

The dependent variable y represents weight of cans in lbs after x weeks from now.

The slope for this model is 20 ( the slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y -intercept).

The model in the form y = mx + b is y = 20x + 200.

By week 12 from now, the weight of cans will be 20*12 + 200 = 240 + 200 = 440 lbs.

If the club has 320lbs of cans after x weeks, then 320 = 20x + 200 or, 20x = 320 - 200 = 120 so that x = 120/20 = 6. Thus, the club will have 320 pounds of cans after 6 weeks.