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Answer :
To solve the problem of finding an equivalent expression for the population equation [tex]\( p = 10000(1.04)^{-t} \)[/tex], we need to rewrite the base [tex]\( 1.04 \)[/tex] in terms of a fraction:
1. Notice the original expression:
[tex]\[
p = 10000(1.04)^{-t}
\][/tex]
This can be rewritten as:
[tex]\[
p = 10000\left(\frac{1}{1.04}\right)^t
\][/tex]
2. The challenge is to find a fraction equivalent to [tex]\(\frac{1}{1.04}\)[/tex] that matches one of the given choices:
To do this, you observe that:
[tex]\[
1.04 \approx \frac{26}{25}
\][/tex]
Therefore, using the fraction:
[tex]\[
\frac{1}{1.04} \approx \frac{25}{26}
\][/tex]
3. Replace the base in the original equation with this fraction:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
This expression is equivalent to the given population equation, and thus the correct choice is:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
1. Notice the original expression:
[tex]\[
p = 10000(1.04)^{-t}
\][/tex]
This can be rewritten as:
[tex]\[
p = 10000\left(\frac{1}{1.04}\right)^t
\][/tex]
2. The challenge is to find a fraction equivalent to [tex]\(\frac{1}{1.04}\)[/tex] that matches one of the given choices:
To do this, you observe that:
[tex]\[
1.04 \approx \frac{26}{25}
\][/tex]
Therefore, using the fraction:
[tex]\[
\frac{1}{1.04} \approx \frac{25}{26}
\][/tex]
3. Replace the base in the original equation with this fraction:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
This expression is equivalent to the given population equation, and thus the correct choice is:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
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