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Answer :
To solve this problem, we're looking for an expression equivalent to [tex]\( p = 10000(1.04)^{-t} \)[/tex].
The problem involves understanding that the expression involves an exponential function with a negative exponent, indicating decay. Here's how we can simplify the given options:
1. Original expression: [tex]\( 1.04^{-t} \)[/tex]
2. Let's compare the given answer choices by rewriting them for understanding:
- [tex]\( \left(\frac{1}{25}\right)^t = (25^{-1})^t = 25^{-t} \)[/tex]
- [tex]\( \left(\frac{25}{26}\right)^t = \left(\frac{25}{26}\right)^t \)[/tex]
- [tex]\( \left(\frac{26}{25}\right)^t = \left(\frac{26}{25}\right)^t \)[/tex]
- [tex]\( \left(\frac{25}{1}\right)^t = 25^t \)[/tex]
3. Now, let's find which rewritten expression results in an equivalent form of [tex]\( 1.04^{-t} \)[/tex]. To do this, consider:
- We want something equivalent to [tex]\( 1.04 = \frac{26}{25} \)[/tex].
- If you divide 26 by 25, you'll find that the approximate value is 1.04.
Therefore, the equivalent expression is [tex]\( 10000\left(\frac{26}{25}\right)^t \)[/tex].
So the correct answer is [tex]\[ p = 10000\left(\frac{26}{25}\right)^t \][/tex].
The problem involves understanding that the expression involves an exponential function with a negative exponent, indicating decay. Here's how we can simplify the given options:
1. Original expression: [tex]\( 1.04^{-t} \)[/tex]
2. Let's compare the given answer choices by rewriting them for understanding:
- [tex]\( \left(\frac{1}{25}\right)^t = (25^{-1})^t = 25^{-t} \)[/tex]
- [tex]\( \left(\frac{25}{26}\right)^t = \left(\frac{25}{26}\right)^t \)[/tex]
- [tex]\( \left(\frac{26}{25}\right)^t = \left(\frac{26}{25}\right)^t \)[/tex]
- [tex]\( \left(\frac{25}{1}\right)^t = 25^t \)[/tex]
3. Now, let's find which rewritten expression results in an equivalent form of [tex]\( 1.04^{-t} \)[/tex]. To do this, consider:
- We want something equivalent to [tex]\( 1.04 = \frac{26}{25} \)[/tex].
- If you divide 26 by 25, you'll find that the approximate value is 1.04.
Therefore, the equivalent expression is [tex]\( 10000\left(\frac{26}{25}\right)^t \)[/tex].
So the correct answer is [tex]\[ p = 10000\left(\frac{26}{25}\right)^t \][/tex].
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