Review for First part (section 007)
- Determine the slope and intercept of the line with equation
- The amount of murders in the city of Detroit is increasing. In the year 2008, 409 people were killed. In 2012, this number increased to 747.
- Assuming that the amount of murders is a linear function of time, find a formula for this functions by finding the equation of the line through these two points.
- Use this formula to predict the amount of murders in the year 2016.
- According to this formula, in what year will the entire city of Detroit have been murdered (all 43,642 people)?
- Consider the function
- Find the average rate of change between and
- Graph and represent the previous average rate of change as the slope of a line
- Which is smaller, the average rate of change of the function between and or the average rate of change between and ?
- A baseball is thrown into the air. The height of the baseball increases at first, and then decreases. The following table records the height at different times:
(seconds) 0 1 2 3 4 5 6 7 (inches) 6 32 69 75 67 49 15 0
Find the average rate of change of the height of the baseball during the first four seconds. Give units and interpret your answers.
- Find the relative change in price given a $3 increase to the cost of each item:
- A gallon of gas costing $2.85
- A pair of shoes costing $95
- On May 4th, 2013, the cost of a stamp was increased from 43 cents to 46 cents. Find the relative rate of change in the cost.
- You know that in ten years you will need to have 45,000 dollars in your savings account. Assuming that the interest rate is 4% and it is compounded continuously, how much should you deposit now?
- A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour. Write a formula for the amount in mg, of caffeine remaining in the body after hours.
- A city’s population is 8,000 and it is growing at a rate of 7% (Note from instructor: “per year?”). Find a formula for the population at time years from now, assuming that the 7% increase is
- An annual rate
- A continuous rate
- A company has a cost and revenue functions, in dollars, given by ,
- Find the cost and revenue if the company produces 1,500 units. Does the company make a profit? What about 400 units?
- Find the break-even point. Illustrate it on a graph.