User:J D Bowen/Midterm

1)

Suppose that in 1920, 20 million people had cars in the United States. Suppose that by 1950, 100 million people had cars.

How many more people got cars every year? Can you graph the increase in car ownership over time? Note that when the car was first invented, only 1 person would have had a car - the inventor! Can you use your equation for car ownership to estimate when the car was invented?

2)

Suppose that as of today, day 0, a telephone-line erecting project had erected 300 miles of telephone wire, and that 1/8 of a mile of wire is erected every day. How much wire will be erected by the end of this week, ie, day 7? Suppose the total length of the telephone wire route is 1000 miles. When will the project be complete? Graph this situation.

3)

Given the equation $$6y-3x=8 \ $$, find the intercepts and slope. Graph this equation.

4)

A mining company plans to extract 850 tons of ore from a mine over the course of one week (7 days). Graph the amount of ore that has been extracted, and the amount that remains in the mine, as functions of time. What are the slopes of these graphs? What do they represent?

5)

Can you factor $$x^2+11x-60 \ $$? List all the values of $$A \ $$ for which $$x^2+Ax-60 \ $$ is factorable.

EXTRA CREDIT:

In problem 4, we described ore mining as a function of time. At some point, there was twice as much ore in the mine as had been extracted. Can you say when this occurred?

EXTRA CREDIT:

Can you use our rules for taking exponents to describe what $$x^{1/2} \ $$ means?