Consider the tables created using an initial investment of \$1,000 and quarterly compounding of interest.
Table A represents the function that models the total amount of one investment, $a(x)$, based on the annual interest rate, $x$, as a percent.
Table B represents the function that models the interest rate, $r(d)$, as a percent, based on the total amount at the end of the investment, $d$.
\begin{table}
\captionsetup{labelformat=empty}
\caption{Table A}
$x$0.75 1 1.25
$a(x)$1,038.18 1,051.21 1,064.39
\end{table}
\begin{table}
\captionsetup{labelformat=empty}
\caption{Table B}
$d$1,057.81 1,077.78 1,098.12
$r(d)$0.75 1 1.25
\end{table}
Use the values in the table to verify the relationship between the functions representing the investments. Which conclusion can be made?
AThe functions are inverses because the domain of Table A is the same as the range of Table B.
BThe functions are inverses because the range of Table A is different from the domain of Table B.
CThe functions are not inverses because for each ordered pair ($x, y$) for one function, there is no corresponding ordered pair ($x, y$) for the other function.
DThe functions are not inverses because for each ordered pair ($x, y$) for one function, there is no corresponding ordered pair ($y, x$) for the other function.
Table A represents the function that models the total amount of one investment, $a(x)$, based on the annual interest rate, $x$, as a percent.
Table B represents the function that models the interest rate, $r(d)$, as a percent, based on the total amount at the end of the investment, $d$.
\begin{table}
\captionsetup{labelformat=empty}
\caption{Table A}
$x$ | 0.75 | 1 | 1.25 |
$a(x)$ | 1,038.18 | 1,051.21 | 1,064.39 |
$d$ | 1,057.81 | 1,077.78 | 1,098.12 |
$r(d)$ | 0.75 | 1 | 1.25 |
AThe functions are inverses because the domain of Table A is the same as the range of Table B.
BThe functions are inverses because the range of Table A is different from the domain of Table B.
CThe functions are not inverses because for each ordered pair ($x, y$) for one function, there is no corresponding ordered pair ($x, y$) for the other function.
DThe functions are not inverses because for each ordered pair ($x, y$) for one function, there is no corresponding ordered pair ($y, x$) for the other function.