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 find an equivalent expression for the given population equation [tex]\( p = 10000(1.04)^{-t} \)[/tex], let's break down the process step-by-step.
1. Understand the Expression: The original expression given is [tex]\( p = 10000(1.04)^{-t} \)[/tex]. Here, [tex]\( 1.04 \)[/tex] is the base, and the exponent is [tex]\(-t\)[/tex].
2. Rewrite [tex]\( 1.04 \)[/tex]: We want to express [tex]\( 1.04 \)[/tex] in a form that could make the expression clearer. Observe that [tex]\( 1.04 \)[/tex] can be represented as a fraction:
[tex]\( 1.04 = \frac{26}{25} \)[/tex].
This is because [tex]\( 1.04 = 1 + 0.04 = \frac{25}{25} + \frac{1}{25} = \frac{26}{25} \)[/tex].
3. Apply the Negative Exponent Rule: The expression [tex]\( (1.04)^{-t} \)[/tex] becomes [tex]\( \left(\frac{26}{25}\right)^{-t} \)[/tex].
Applying the negative exponent rule, which is [tex]\( a^{-b} = \left(\frac{1}{a}\right)^b \)[/tex], we get:
[tex]\(\left(\frac{26}{25}\right)^{-t} = \left(\frac{1}{\frac{26}{25}}\right)^t = \left(\frac{25}{26}\right)^t\)[/tex].
4. Update the Expression: Substitute back into the original equation with this new base:
[tex]\[
p = 10000 \times \left(\frac{25}{26}\right)^t
\][/tex]
Therefore, the equivalent expression is:
[tex]\[ p = 10000\left(\frac{25}{26}\right)^t \][/tex]
This matches the second option from the multiple-choice answers.
1. Understand the Expression: The original expression given is [tex]\( p = 10000(1.04)^{-t} \)[/tex]. Here, [tex]\( 1.04 \)[/tex] is the base, and the exponent is [tex]\(-t\)[/tex].
2. Rewrite [tex]\( 1.04 \)[/tex]: We want to express [tex]\( 1.04 \)[/tex] in a form that could make the expression clearer. Observe that [tex]\( 1.04 \)[/tex] can be represented as a fraction:
[tex]\( 1.04 = \frac{26}{25} \)[/tex].
This is because [tex]\( 1.04 = 1 + 0.04 = \frac{25}{25} + \frac{1}{25} = \frac{26}{25} \)[/tex].
3. Apply the Negative Exponent Rule: The expression [tex]\( (1.04)^{-t} \)[/tex] becomes [tex]\( \left(\frac{26}{25}\right)^{-t} \)[/tex].
Applying the negative exponent rule, which is [tex]\( a^{-b} = \left(\frac{1}{a}\right)^b \)[/tex], we get:
[tex]\(\left(\frac{26}{25}\right)^{-t} = \left(\frac{1}{\frac{26}{25}}\right)^t = \left(\frac{25}{26}\right)^t\)[/tex].
4. Update the Expression: Substitute back into the original equation with this new base:
[tex]\[
p = 10000 \times \left(\frac{25}{26}\right)^t
\][/tex]
Therefore, the equivalent expression is:
[tex]\[ p = 10000\left(\frac{25}{26}\right)^t \][/tex]
This matches the second option from the multiple-choice answers.
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
