Review for the Fourth part (section 007)

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  1. The velocity of a car is f(t)=3.5t meters/second. Find the exact distance traveled by the car (in meters) from t=0 to t=15.
  2. The value of a mutual fund increases at a rate of R=1700e^{0.07t} dollars per year, where t is years since 2009.
    1. Make a table of values for R using t=0,2,4,6,8,10 (round your answers to two decimal places)
    2. Use the previous table to estimate the total change in the value of the mutual fund between 2009 and 2019. (round your final answer to two decimal places)
    3. Use the actual formula to compute the true total change in the value of the mutual fund between 2009 and 2019.
  3. Find the average of the function f(x)=12+11x-2x^2 between x=0 and x=4.5
  4. The value V of a Tiffany lamp worth $215 in 1975 increases at 26% per year.
    1. Find a formula that expresses the value V as a function of time, t years after 1975.
    2. Use this formula to find the average value of the lamp over the period 1975-2000 (round your answer to the nearest integer)
  5. Compute the area of the region bounded by the lines y=x+18, y=20-3x, x=0 and x=4.
  6. Compute the are of the region bounded by the curves of y=2x^2 and y=4-14x^2
  7. Given the demand curve p=21-q^2 and supply curve p=3+q^2, find the producer surplus when the market is in equilibrium.
  8. Find the consumer surplus for the demand curve p=129-3q when q=10 units.
  9. Supply and demand data are shown in the tables below:

    \begin{tabular}{l|r|r|r|r|r|r|r|} q & 0 & 100 & 200 & 300 & 400 & 500 & 600 \\ \hline p & 13& 16 & 21 & 28 & 33 & 36 & 41 \\ \\ q & 0 & 100 & 200 & 300 & 400 & 500 & 600 \\ \hline p & 52 & 41 & 32 & 28 & 21 & 12 & 9 \end{tabular}

    1. Which table shows the supply, and which shows demand?
    2. Estimate equilibrium price and quantity
    3. Estimate consumer and producer surplus at equilibrium
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