Review for First part (section 008)

Note from the instructor: this exam is amazing! Good job guys! I had to take out some questions that were too repetitive, but even those were really good choices.

  1. The price of a house begins at $40,000. Each year, the house increases in price by $3,175.
    1. Create a function for the increase in price t years after it was built.
    2. How much will the house cost after 17 years?
    3. How many years will it take for the house to reach $125,000? (round to the nearest integer)
  2. Find the intercepts for the following functions:
    1. f(x)=x^2-4
    2. f(x)=e^x-2
  3. The tables below show the increased population (in millions) from 2 different cities between the years 1980 and 1990.

    \begin{tabular}{|r|r|r|r|r|r|} \hline 1980 & 1982 & 1984 & 1986 & 1988 & 1990  \\ \hline 0.96 & 0.99 & 1.01 & 1.2  & 1.25 & 1.345 \\ \hline \end{tabular}

    \begin{tabular}{|r|r|r|r|r|r|} \hline 1980 & 1982 & 1984 & 1986 & 1988 & 1990  \\ \hline 1.72 & 1.85 & 1.87 & 2.01 & 2.23 & 2.495 \\ \hline \end{tabular}

    1. Find the average rate of change for both cities. (note from the instructor: from 1980 to 1990?)
    2. Determine which of the two cities increased the fastest.(note from the instructor: from 1980 to 1990?)
  4. The cost of a pound of chicken increased from $1.99 to $2.79. What is the relative rate of change?
  5. Solve for t:  14=10e^{0.05t}.
  6. A city’s population is 800 and growing at 5% per year.
    1. Find a formula for the population P, at time t years from now assuming that 5% per year is:
      1. An annual rate
      2. A continuous annual rate
    2. For each case in the previous part, estimate the population of the city in 30 years
  7. The supply and demand of baseball caps is given respectively by the equations q=4p-45.5, and q=85-5p. Find equilibrium price and quantity.
  8. A record company spends $900 setting up their equipment and starting the company. A black CD costs 50¢ per CD. They charge $12 per CD. Let q be the number of CDs sold.
    1. What is the record company’s fixed cost?
    2. What is the record company’s variable cost?
    3. What is the cost function (as a function of q)?
    4. Write a formula for their revenue
    5. Write a formula for their profit
    6. What is their break-even point?
    7. How many CDs do they need to sell to make a profit?
  9. The amount of rice grown and sold in the U.S., in billions of pounds, is given by the following table:

    \begin{tabular}{|l|r|r|r|r|r|r|r|} \hline Year       & 1999 & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 \\ \hline  Rice (lbs) &   19 &   22 &   24 &   21 &   23 &   20 &   23 \\ \hline  \end{tabular}

    What is the average rate of change of rice being sold from 1999 to 2005?

  10. Determine the y-intercept of the line with the equation 4x=8y+16.
  1. Brooke Balentine
    April 22, 2013 at 4:16 pm

    For #6 (A) is the percentage 0.05 or 1.05 and how do you know when to add,subtract, or leave it the same as the problem gives you?

    -Brooke Balentine

    • Lauren Baker
      April 25, 2013 at 8:59 pm

      a is 1.05. I think you add because it is saying that the population is growing. I’m not sure if that is exactly what you were asking or not though?

  2. Danielle Long
    April 22, 2013 at 5:23 pm

    For that part it is 1.05 because for just annual rates you have to add the 1
    Then when it is a continuous annual rate you leave it as the decimal of the percentage and don’t add 1 to it.
    Does that help?

    -Danielle Long

    • Brooke Balentine
      April 23, 2013 at 11:18 pm

      Yes, thank you so much!!
      -Brooke Balentine

  3. Avery Ducharme
    April 22, 2013 at 11:30 pm

    what units do you use for ARC

    • Alyssa Aronson
      April 23, 2013 at 8:43 pm

      The ARC for question 3 a’s units are population in millions. Your decimal represents how much the population is increasing over the years.
      Alyssa Aronson

    • Michelle Velez- Martinez
      April 24, 2013 at 1:38 pm

      The units for the ARC question number 9 would be billions of lbs/ year. It represents the average amount of rice being produced over a certain number of years.

  4. April 23, 2013 at 8:24 pm

    Essentially, break-even point is when you set them equal to each other correct?

    • Brooke Balentine
      April 23, 2013 at 11:16 pm

      Yes, that’s correct!
      -Brooke Balentine

      • April 25, 2013 at 9:22 am

        Thanks much!
        Robbie Dean

  5. Alyssa Aronson
    April 23, 2013 at 8:46 pm

    Is the formula for profit = revenue – cost or cost- revenue ?

    • Rayshonda perry
      April 23, 2013 at 11:22 pm

      Profit = revenue – cost.

  6. Kellie Hafko
    April 23, 2013 at 11:00 pm

    I wasn’t quite sure how to do question 2… would you solve for the intercepts like you do in question 10, or are you trying to get actual coordinates?

    • Michelle Velez- Martinez
      April 24, 2013 at 1:39 pm

      For number 2, all you have to do is just solve for the intercepts. To solve for x, set the equation equal to zero. To solve for y, set x equal to zero.

  7. Morgan Leiter
    April 23, 2013 at 11:58 pm

    For number 10, to find the y-intercept, I got y=2 by putting the equation all over 8 and moving the y to one side. I got y=2 by setting the x equal to 0. Is the answer just 2 or is it y=±2? because I was looking online and they mostly had the answer as y=±2.
    -Morgan Leiter

    • Michelle Velez- Martinez
      April 24, 2013 at 1:40 pm

      The answer is y=±2 because you end up taking the square root of 4.

  8. Karlina Nichols
    April 24, 2013 at 12:43 am

    Is the relative rate of change y1-y0 divided by y0 or y1-y0 divided by y1?

    • Nicholas Long
      April 24, 2013 at 9:58 am

      The relative change is y1-y0 divided by y0.

  9. Avery Ducharme
    April 29, 2013 at 6:16 pm

    what is the formula for relative rate of change?

    • Lauren Bennett
      April 30, 2013 at 1:53 pm

      The formula for relative rate of change of a function f(x) is f′(x) divided by f(x).

  10. Carly Gillet
    May 1, 2013 at 8:46 pm

    For #8 b, would you just write 50 cents as the variable cost? Does he just want that alone? or should I write 50x?

  11. Carly Gillet
    May 1, 2013 at 8:51 pm

    Also, whenever you see “continuous” does that mean you are using the growth formula with e? so Pe^rt is continuous?

  12. Matt Stesienko
    May 2, 2013 at 4:26 pm

    Carly- When something is “compounded continuously” in a problem, you are to use the formula: P=Pe^rt. The ‘P’ is your initial value or amount, “R” is the rate at which you are compounding, and “T” is the duration of time. All are usually given in the problem, we just need to know when to use each of the formulas.

    • Matt Stesienko
      May 2, 2013 at 4:31 pm

      Also, a really good example he gave us was the one about “winning 1 million dollars through the lottery and you could choose 4 yearly installments or one lump sum.” This example is in our class notes from 2/4/13. The problem is really effective because it illustrates each method. I’d definitely revisit that example, if you need help with it.

  13. Catherine helms
    May 2, 2013 at 11:45 pm

    For #6 part ii. what is the value of k?

  14. Christina Gleaton
    May 3, 2013 at 1:04 pm

    For number 6, you must add 1 and .05 correct? I know that sometimes you subtract but you add here? How do you know when to add or subtract?

  15. Christina Gleaton
    May 3, 2013 at 1:06 pm

    Is the average rate of change expressed as a percentage?

  16. Tucker Griffin
    May 3, 2013 at 2:03 pm

    Christina, the ARC is not expressed as a percentage. However, the relative change is usually expressed as a percentage.
    Tucker Griffin

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