Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To solve the problem, we need to find the ratio of the total value of Adele's account to Leela's account and express this ratio as a percentage.
1. Determine the value of Leela's account after \( t \) years:
The formula for the value of Leela's account is given by:
[tex]\[ V_l = 500 (1.045)^t \][/tex]
2. Determine the value of Adele's account after \( t \) years:
Since Adele begins investing two years earlier, the formula for the value of Adele's account after \( t \) years is:
[tex]\[ V_e = 500 (1.045)^{t+2} \][/tex]
3. Calculate the ratio of \( V_e \) to \( V_l \):
To find how much Adele's account is compared to Leela's, we take the ratio of \( V_e \) to \( V_l \):
[tex]\[ \text{Ratio} = \frac{V_e}{V_l} = \frac{500 (1.045)^{t+2}}{500 (1.045)^t} \][/tex]
4. Simplify the ratio:
Notice that the \( 500 \) terms cancel out:
[tex]\[ \text{Ratio} = \frac{(1.045)^{t+2}}{(1.045)^t} \][/tex]
Using the properties of exponents, specifically \((a^{m+n} = a^m \cdot a^n)\),
[tex]\[ \text{Ratio} = \frac{(1.045)^t \cdot (1.045)^2}{(1.045)^t} = (1.045)^2 \][/tex]
5. Calculate \( (1.045)^2 \):
[tex]\[ (1.045)^2 = 1.045 \times 1.045 = 1.092025 \][/tex]
6. Convert the ratio to a percentage:
To express the ratio as a percentage, multiply by 100:
[tex]\[ \text{Percentage} = 1.092025 \times 100 \approx 109.2\% \][/tex]
So, the total value of Adele's account is approximately \( 109.2\% \) of the total value of Leela's account at any time \( t \).
The correct answer is:
[tex]\( \boxed{109.2\%} \)[/tex]
1. Determine the value of Leela's account after \( t \) years:
The formula for the value of Leela's account is given by:
[tex]\[ V_l = 500 (1.045)^t \][/tex]
2. Determine the value of Adele's account after \( t \) years:
Since Adele begins investing two years earlier, the formula for the value of Adele's account after \( t \) years is:
[tex]\[ V_e = 500 (1.045)^{t+2} \][/tex]
3. Calculate the ratio of \( V_e \) to \( V_l \):
To find how much Adele's account is compared to Leela's, we take the ratio of \( V_e \) to \( V_l \):
[tex]\[ \text{Ratio} = \frac{V_e}{V_l} = \frac{500 (1.045)^{t+2}}{500 (1.045)^t} \][/tex]
4. Simplify the ratio:
Notice that the \( 500 \) terms cancel out:
[tex]\[ \text{Ratio} = \frac{(1.045)^{t+2}}{(1.045)^t} \][/tex]
Using the properties of exponents, specifically \((a^{m+n} = a^m \cdot a^n)\),
[tex]\[ \text{Ratio} = \frac{(1.045)^t \cdot (1.045)^2}{(1.045)^t} = (1.045)^2 \][/tex]
5. Calculate \( (1.045)^2 \):
[tex]\[ (1.045)^2 = 1.045 \times 1.045 = 1.092025 \][/tex]
6. Convert the ratio to a percentage:
To express the ratio as a percentage, multiply by 100:
[tex]\[ \text{Percentage} = 1.092025 \times 100 \approx 109.2\% \][/tex]
So, the total value of Adele's account is approximately \( 109.2\% \) of the total value of Leela's account at any time \( t \).
The correct answer is:
[tex]\( \boxed{109.2\%} \)[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.