Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To determine which statement is true about the two investments during the first three years, let's analyze the given information and find the average rates of change for both investments.
### Investment A:
- The initial value of investment A is 2,000 dollars.
- The average rate of change for investment A over the interval [tex]\([0, 3]\)[/tex] is -95.1 dollars per year.
An average rate of change of -95.1 indicates that investment A is decreasing in value because the rate of change is negative.
### Investment B:
- The table provides the values of investment B at different years:
[tex]\[ \begin{array}{|c|c|} \hline x & g(x) \\ \hline 0 & 1800 \\ \hline 1 & 1710 \\ \hline 2 & 1624 \\ \hline 3 & 1543 \\ \hline \end{array} \][/tex]
To find the average rate of change for investment B over the interval [tex]\([0, 3]\)[/tex]:
[tex]\[ \text{Average Rate of Change for B} = \frac{g(3) - g(0)}{3 - 0} \][/tex]
Substituting the values from the table:
[tex]\[ \text{Average Rate of Change for B} = \frac{1543 - 1800}{3} = \frac{-257}{3} \approx -85.67 \text{ dollars per year} \][/tex]
An average rate of change of approximately -85.67 indicates that investment B is also decreasing in value because the rate of change is negative.
### Comparison:
Since both investments have a negative average rate of change, both investments are decreasing in value over the first three years.
- For investment A, the average rate of decrease is -95.1 dollars per year.
- For investment B, the average rate of decrease is approximately -85.67 dollars per year.
Given that the magnitude of the average rate of decrease for investment A ([tex]\(|-95.1|\)[/tex]) is greater than that of investment B ([tex]\(|-85.67|\)[/tex]), investment A is decreasing in value faster than investment B.
### Conclusion:
Based on this analysis, the correct statement is:
C. Both investments are decreasing in value, and investment A is decreasing in value faster.
### Investment A:
- The initial value of investment A is 2,000 dollars.
- The average rate of change for investment A over the interval [tex]\([0, 3]\)[/tex] is -95.1 dollars per year.
An average rate of change of -95.1 indicates that investment A is decreasing in value because the rate of change is negative.
### Investment B:
- The table provides the values of investment B at different years:
[tex]\[ \begin{array}{|c|c|} \hline x & g(x) \\ \hline 0 & 1800 \\ \hline 1 & 1710 \\ \hline 2 & 1624 \\ \hline 3 & 1543 \\ \hline \end{array} \][/tex]
To find the average rate of change for investment B over the interval [tex]\([0, 3]\)[/tex]:
[tex]\[ \text{Average Rate of Change for B} = \frac{g(3) - g(0)}{3 - 0} \][/tex]
Substituting the values from the table:
[tex]\[ \text{Average Rate of Change for B} = \frac{1543 - 1800}{3} = \frac{-257}{3} \approx -85.67 \text{ dollars per year} \][/tex]
An average rate of change of approximately -85.67 indicates that investment B is also decreasing in value because the rate of change is negative.
### Comparison:
Since both investments have a negative average rate of change, both investments are decreasing in value over the first three years.
- For investment A, the average rate of decrease is -95.1 dollars per year.
- For investment B, the average rate of decrease is approximately -85.67 dollars per year.
Given that the magnitude of the average rate of decrease for investment A ([tex]\(|-95.1|\)[/tex]) is greater than that of investment B ([tex]\(|-85.67|\)[/tex]), investment A is decreasing in value faster than investment B.
### Conclusion:
Based on this analysis, the correct statement is:
C. Both investments are decreasing in value, and investment A is decreasing in value faster.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.