Explore IDNLearn.com to discover insightful answers from experts and enthusiasts alike. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.
Sagot :
To determine the best statement that represents the domain of the function [tex]\( j(t) \)[/tex], we need to understand what the domain represents in this context. The domain of a function is the set of all possible input values (in this case, the variable [tex]\( t \)[/tex]) for which the function is defined.
Juanita deposits $500 into a savings account that earns 1.5% interest annually, compounded once per year. The function [tex]\( j(t) \)[/tex] represents the amount of money in her account [tex]\( t \)[/tex] years after opening the account.
### Step-by-Step:
1. Understanding [tex]\( t \)[/tex]:
- [tex]\( t \)[/tex] represents the number of years after she has made the initial deposit.
- Since time cannot be negative, [tex]\( t \)[/tex] must be non-negative.
- Additionally, since interest is compounded annually, [tex]\( t \)[/tex] should be measured in whole years (0, 1, 2, etc.).
2. Constraints on [tex]\( t \)[/tex]:
- [tex]\( t \geq 0 \)[/tex] because she cannot have opened the account in negative time.
- [tex]\( t \)[/tex] should be a whole number because the compounding happens annually (we can't have fractional years for our input).
Now, let's analyze the given options:
1. [tex]\( t \geq 500 \)[/tex]:
- This is incorrect because it incorrectly implies [tex]\( t \)[/tex] needs to be at least 500 years, which doesn't make sense for the problem.
2. the set of integers:
- While positive integers could be part of the domain, this includes negative integers which do not make sense in this context because [tex]\( t \)[/tex] cannot be negative.
3. [tex]\( t \geq 500 + 500 \cdot 1.5 \%\)[/tex]:
- This suggests a specific starting value for [tex]\( t \)[/tex] that depends on the interest calculation, which is irrelevant to defining the valid input for [tex]\( t \)[/tex]. The function's domain isn't defined by the specific interest-based amount but by possible values of [tex]\( t \)[/tex].
4. the set of whole numbers:
- This is correct. It accurately states that [tex]\( t \)[/tex] must be 0 or any positive whole number (1, 2, 3, etc.).
### Conclusion:
The statement that best represents the domain of the function [tex]\( j(t) \)[/tex] is:
The set of whole numbers.
This means [tex]\( t \)[/tex] can be any non-negative integer (0, 1, 2, 3, ...).
Juanita deposits $500 into a savings account that earns 1.5% interest annually, compounded once per year. The function [tex]\( j(t) \)[/tex] represents the amount of money in her account [tex]\( t \)[/tex] years after opening the account.
### Step-by-Step:
1. Understanding [tex]\( t \)[/tex]:
- [tex]\( t \)[/tex] represents the number of years after she has made the initial deposit.
- Since time cannot be negative, [tex]\( t \)[/tex] must be non-negative.
- Additionally, since interest is compounded annually, [tex]\( t \)[/tex] should be measured in whole years (0, 1, 2, etc.).
2. Constraints on [tex]\( t \)[/tex]:
- [tex]\( t \geq 0 \)[/tex] because she cannot have opened the account in negative time.
- [tex]\( t \)[/tex] should be a whole number because the compounding happens annually (we can't have fractional years for our input).
Now, let's analyze the given options:
1. [tex]\( t \geq 500 \)[/tex]:
- This is incorrect because it incorrectly implies [tex]\( t \)[/tex] needs to be at least 500 years, which doesn't make sense for the problem.
2. the set of integers:
- While positive integers could be part of the domain, this includes negative integers which do not make sense in this context because [tex]\( t \)[/tex] cannot be negative.
3. [tex]\( t \geq 500 + 500 \cdot 1.5 \%\)[/tex]:
- This suggests a specific starting value for [tex]\( t \)[/tex] that depends on the interest calculation, which is irrelevant to defining the valid input for [tex]\( t \)[/tex]. The function's domain isn't defined by the specific interest-based amount but by possible values of [tex]\( t \)[/tex].
4. the set of whole numbers:
- This is correct. It accurately states that [tex]\( t \)[/tex] must be 0 or any positive whole number (1, 2, 3, etc.).
### Conclusion:
The statement that best represents the domain of the function [tex]\( j(t) \)[/tex] is:
The set of whole numbers.
This means [tex]\( t \)[/tex] can be any non-negative integer (0, 1, 2, 3, ...).
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.
