MATH 122 Fall 2014 Review Exam (4|4)

There were way too many repetitive examples, and some of the questions did not even have a statement—just a table, but no indication of what to do with it. Among the repeated types of questions, I selected what I considered the most interesting, and avoided to include the rest.
I would have liked to see at least one example of one definite integral that cannot be completed with the calculator, especially if the integration technique is a substitution.
  1. With \( t \) years since 2000, the population, \( P \), of the world in billions can be modeled by \( P=6.1e^{.012t} \)
    • What was the population in 2013?
    • What will be the population in 2025?
    • Find the average population of the world between 2000 and 2011.
  2. If \( t \) is time in years, and \( t=0 \) represents January 1, 2005, worldwide energy consumption, \( r \), in quadrillion (\( 10^{15}\)) BTUs per year, is modeled by, \( r = 461e^{.0185t} \).
    • Write a definite integral for the total energy use between the start of 2005 and the start of 2017.
    • Use the Fundamental Theorem of Calculus to evaluate the integral. Round to the nearest integer.
  3. Compute the following definite integral:

    \begin{equation} \int_1^4 \big( 3^x + \tfrac{3}{x} \big)\, dx \end{equation}
  4. War Emblem, winner of the 2002 Kentucky Derby, can reach up to the speed of 50mph. His speed was clocked every 30 seconds. The results are in the table below. What was his average speed?

    Time (Seconds)0306090120
    Speed (mph)040383537
  5. The following table gives the number of likes, \( L \), that Amanda gets on her instagram post per hour. Let \( t \) be the number of hours since the post and \( L=f(t) \). What is the average number of likes that Amanda got in the first 6 hours?

  6. Find the net area of the function \( y= f(x) = -2 + 5x \) between \( x=0 \) and \( x=4 \)
  7. The following table gives the emissions \( E \) of nitrogen oxide in millions of metric tons per year in the US Let \( t \) be the number of years since 1970 and \( E = f(t) \).

    E 26.926.4 27.1 25.8 25.5 25.9 22.6
    • What are the units and meaning of \( \int_0^{30} f(t)\, dt \)?
    • Estimate the previous integral.