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Answer :
To find which of the given expressions is equivalent to [tex]\( p = 10000(1.04)^{-t} \)[/tex], we need to transform the original expression:
1. The original expression is [tex]\( p = 10000(1.04)^{-t} \)[/tex].
2. The [tex]\( (1.04)^{-t} \)[/tex] part means that we take the reciprocal of 1.04 and raise it to the power of [tex]\( t \)[/tex]. So, we need to rewrite this as:
[tex]\[
(1.04)^{-t} = \left(\frac{1}{1.04}\right)^t
\][/tex]
3. To find [tex]\(\frac{1}{1.04}\)[/tex], we calculate:
[tex]\[
\frac{1}{1.04} \approx 0.9615
\][/tex]
4. We can approximate this reciprocal to a fraction. The fraction closest to 0.9615 that also simplifies nicely is [tex]\(\frac{25}{26}\)[/tex], because:
[tex]\[
\frac{25}{26} \approx 0.9615
\][/tex]
5. So, the expression becomes:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
Therefore, the equivalent expression to [tex]\( p = 10000(1.04)^{-t} \)[/tex] is:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
The correct choice is:
[tex]\( p = 10000\left(\frac{25}{26}\right)^t \)[/tex]
1. The original expression is [tex]\( p = 10000(1.04)^{-t} \)[/tex].
2. The [tex]\( (1.04)^{-t} \)[/tex] part means that we take the reciprocal of 1.04 and raise it to the power of [tex]\( t \)[/tex]. So, we need to rewrite this as:
[tex]\[
(1.04)^{-t} = \left(\frac{1}{1.04}\right)^t
\][/tex]
3. To find [tex]\(\frac{1}{1.04}\)[/tex], we calculate:
[tex]\[
\frac{1}{1.04} \approx 0.9615
\][/tex]
4. We can approximate this reciprocal to a fraction. The fraction closest to 0.9615 that also simplifies nicely is [tex]\(\frac{25}{26}\)[/tex], because:
[tex]\[
\frac{25}{26} \approx 0.9615
\][/tex]
5. So, the expression becomes:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
Therefore, the equivalent expression to [tex]\( p = 10000(1.04)^{-t} \)[/tex] is:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
The correct choice is:
[tex]\( p = 10000\left(\frac{25}{26}\right)^t \)[/tex]
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