Review for First part (section 007)

  1. Determine the slope and y-intercept of the line with equation 3y+12x-1=0.
  2. 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.
    1. 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.
    2. Use this formula to predict the amount of murders in the year 2016.
    3. According to this formula, in what year will the entire city of Detroit have been murdered (all 43,642 people)?
  3. Consider the function y=f(x)=\sqrt{x}.
    1. Find the average rate of change between x=3 and x=7.
    2. Graph f(x) and represent the previous average rate of change as the slope of a line
    3. Which is smaller, the average rate of change of the function between x=3 and x=4, or the average rate of change between x=4 and x=6?
  4. 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:
    t (seconds) 0 1 2 3 4 5 6 7
    h (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.

  5. Find the relative change in price given a $3 increase to the cost of each item:
    1. A gallon of gas costing $2.85
    2. A pair of shoes costing $95
  6. 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.
  7. 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?
  8. 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 A in mg, of caffeine remaining in the body after t hours.
  9. 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 P at time t years from now, assuming that the 7% increase is
    1. An annual rate
    2. A continuous rate
  10. A company has a cost and revenue functions, in dollars, given by C(q) = 16,000+40q, R(q)=42q
    1. Find the cost and revenue if the company produces 1,500 units. Does the company make a profit? What about 400 units?
    2. Find the break-even point. Illustrate it on a graph.
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