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Answer :
We start with the given equation:
[tex]$$
p = 10000(1.04)^{-t}.
$$[/tex]
Recall that raising a number to a negative exponent is equivalent to taking the reciprocal raised to the positive exponent. That is,
[tex]$$
(1.04)^{-t} = \left(\frac{1}{1.04}\right)^t.
$$[/tex]
Next, we express [tex]$1.04$[/tex] as a fraction. Notice that
[tex]$$
1.04 = \frac{26}{25}.
$$[/tex]
Taking the reciprocal gives:
[tex]$$
\frac{1}{1.04} = \frac{1}{\frac{26}{25}} = \frac{25}{26}.
$$[/tex]
Substitute this back into the equation:
[tex]$$
p = 10000\left(\frac{25}{26}\right)^t.
$$[/tex]
Thus, the equivalent expression is
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t,
\][/tex]
which corresponds to the second option.
[tex]$$
p = 10000(1.04)^{-t}.
$$[/tex]
Recall that raising a number to a negative exponent is equivalent to taking the reciprocal raised to the positive exponent. That is,
[tex]$$
(1.04)^{-t} = \left(\frac{1}{1.04}\right)^t.
$$[/tex]
Next, we express [tex]$1.04$[/tex] as a fraction. Notice that
[tex]$$
1.04 = \frac{26}{25}.
$$[/tex]
Taking the reciprocal gives:
[tex]$$
\frac{1}{1.04} = \frac{1}{\frac{26}{25}} = \frac{25}{26}.
$$[/tex]
Substitute this back into the equation:
[tex]$$
p = 10000\left(\frac{25}{26}\right)^t.
$$[/tex]
Thus, the equivalent expression is
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t,
\][/tex]
which corresponds to the second option.
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