4.7.1: Practice Problems Corequisite N.7
- Page ID
- 148611
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Let's say the minimum wage in 1994 was $5.25 per hour. The minimum wage in 2021 was $7.25 per hour.
(1) What was the absolute change in the minimum wage from 1994 to 2021?
(2) What was the relative change in the minimum wage from 1994 to 2021? Round to the nearest tenth of one percent.
(3) If the average price of a movie ticket in 1994 was $6.24, which statement is correct?
(i) In 1994, a person earning minimum wage had to work less than an hour to earn enough for a movie ticket.
(ii) In 1994, a person earning minimum wage had to work more than an hour to earn enough for a movie ticket.
(4) If the average price of a movie ticket in 2021 was $6.24, which statement is correct?
(i) In 2021, a person earning minimum wage had to work more than an hour to earn enough for a movie ticket.
(ii) In 2021, a person earning minimum wage had to work less than an hour to earn enough for a movie ticket.
For the questions below refer to the CPI-U table.
This table gives the cost of a representative basket of goods and services in base-year dollars (1983). The table shows the indices for selected years from 1913 to 2021. The Consumer Price Index (CPI-U) provides an indication of how the price of consumer goods changes over time.
Let's say that in 1999, a standard cup of coffee cost $1.48. In 2021, that same cup of coffee was $2.55.
(5) What was the relative increase in the price of the cup of coffee from 1999 to 2021? Round to the nearest one percent.
(6) What was the relative increase in the CPI-U from 1999 to 2021? Round to the nearest one percent.
(7) Which of the following statements is true?
(i) From 1999 to 2021, the price of coffee increased at a higher rate than the CPI-U.
(ii) From 1999 to 2021, the price of coffee increased at a lower rate than the CPI-U.
(iii) From 1999 to 2021, the price of coffee increased at the same rate as the CPI-U.
(8) The rent on a building in 1997 was $1,300 per month. The landlord changes the rent relative to changes in the CPI-U. Use the CPI-U to calculate the rent in 2000. Round to the nearest dollar.