We appreciate your visit to The population tex p tex of a town after tex t tex years is represented using the equation tex p 10000 1 04 t tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve this problem, we need to find an expression equivalent to the given population model:
[tex]\[ p = 10000(1.04)^{-t} \][/tex]
Let's break this down step by step:
1. Understand the Original Expression:
- The original equation given is [tex]\( p = 10000(1.04)^{-t} \)[/tex].
- The expression involves an exponent with a negative sign: [tex]\((1.04)^{-t}\)[/tex].
2. Rewrite the Negative Exponent:
- A negative exponent means taking the reciprocal of the base and reversing the sign of the exponent.
- Therefore, [tex]\((1.04)^{-t} = \left(\frac{1}{1.04}\right)^t\)[/tex].
3. Simplify the Base:
- We need to simplify the base [tex]\(\frac{1}{1.04}\)[/tex].
- Divide 1 by 1.04:
[tex]\[
\frac{1}{1.04} = 0.9615384615 \, \text{(approx.)}
\][/tex]
4. Convert Decimal to Fraction:
- The decimal 0.961538... is equivalent to the fraction [tex]\(\frac{25}{26}\)[/tex].
5. Substitute Back:
- Substituting back to the expression, we have:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
6. Select the Equivalent Expression:
- From the given options, choose the expression that matches:
[tex]\[
p=10000\left(\frac{25}{26}\right)^t
\][/tex]
Therefore, the equivalent expression is:
[tex]\[ p = 10000\left(\frac{25}{26}\right)^t \][/tex]
This corresponds to the option: [tex]\( p=10000\left(\frac{25}{26}\right)^{,} \)[/tex] (Note: It seems there might be a typo in the option itself, but the mathematical representation matches our derived expression).
[tex]\[ p = 10000(1.04)^{-t} \][/tex]
Let's break this down step by step:
1. Understand the Original Expression:
- The original equation given is [tex]\( p = 10000(1.04)^{-t} \)[/tex].
- The expression involves an exponent with a negative sign: [tex]\((1.04)^{-t}\)[/tex].
2. Rewrite the Negative Exponent:
- A negative exponent means taking the reciprocal of the base and reversing the sign of the exponent.
- Therefore, [tex]\((1.04)^{-t} = \left(\frac{1}{1.04}\right)^t\)[/tex].
3. Simplify the Base:
- We need to simplify the base [tex]\(\frac{1}{1.04}\)[/tex].
- Divide 1 by 1.04:
[tex]\[
\frac{1}{1.04} = 0.9615384615 \, \text{(approx.)}
\][/tex]
4. Convert Decimal to Fraction:
- The decimal 0.961538... is equivalent to the fraction [tex]\(\frac{25}{26}\)[/tex].
5. Substitute Back:
- Substituting back to the expression, we have:
[tex]\[
p = 10000\left(\frac{25}{26}\right)^t
\][/tex]
6. Select the Equivalent Expression:
- From the given options, choose the expression that matches:
[tex]\[
p=10000\left(\frac{25}{26}\right)^t
\][/tex]
Therefore, the equivalent expression is:
[tex]\[ p = 10000\left(\frac{25}{26}\right)^t \][/tex]
This corresponds to the option: [tex]\( p=10000\left(\frac{25}{26}\right)^{,} \)[/tex] (Note: It seems there might be a typo in the option itself, but the mathematical representation matches our derived expression).
Thanks for taking the time to read The population tex p tex of a town after tex t tex years is represented using the equation tex p 10000 1 04 t tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
