Question
An algorithm on a social media site is set up so that the more shares a video receives, the more individuals the video is presented to on their feed. The views of a particular video are increasing at an exponential rate of 100% for each share the video receives. If the video originated with 10 views, the situation can be modeled by the exponential equation v(s)=10(2)s
where v is the number of views for every s shares. Which of the following statements is true about the equation?
(1 point)
Responses
The domain (s-values) is all real numbers.
The domain (s-values) is all real numbers. - no response given
The range (v-values) includes the values greater than (0<v≤10)
.
The range (v-values) includes the values greater than (0<v≤10)
. - incorrect
The domain (s-values) includes the values (s≥0)
.
The domain (s-values) includes the values open paren s is greater than or equal to 0 close paren. - no response given
The range (v-values) is all real numbers.
where v is the number of views for every s shares. Which of the following statements is true about the equation?
(1 point)
Responses
The domain (s-values) is all real numbers.
The domain (s-values) is all real numbers. - no response given
The range (v-values) includes the values greater than (0<v≤10)
.
The range (v-values) includes the values greater than (0<v≤10)
. - incorrect
The domain (s-values) includes the values (s≥0)
.
The domain (s-values) includes the values open paren s is greater than or equal to 0 close paren. - no response given
The range (v-values) is all real numbers.
Answers
GPT-4o mini
To analyze the equation \( v(s) = 10(2)^s \), we need to determine the valid domain and range of the function.
1. **Domain**:
- \( s \) represents the number of shares. Since you cannot have a negative number of shares in this context, the domain is \( s \geq 0 \).
- Therefore, the statement "The domain (s-values) includes the values \( s \geq 0 \)" is **true**.
2. **Range**:
- When \( s = 0 \): \( v(0) = 10(2^0) = 10 \).
- As \( s \) increases, since \( 2^s \) grows exponentially, \( v(s) \) will also increase without bound. Hence, the range of \( v(s) \) starts from 10 and goes to infinity.
- Therefore, the range is \( v \geq 10 \) (all values greater than or equal to 10).
- The statements about the range including values less than 10 or being all real numbers are **incorrect**.
Conclusively, the correct statement is: **The domain (s-values) includes the values \( s \geq 0 \)**.
1. **Domain**:
- \( s \) represents the number of shares. Since you cannot have a negative number of shares in this context, the domain is \( s \geq 0 \).
- Therefore, the statement "The domain (s-values) includes the values \( s \geq 0 \)" is **true**.
2. **Range**:
- When \( s = 0 \): \( v(0) = 10(2^0) = 10 \).
- As \( s \) increases, since \( 2^s \) grows exponentially, \( v(s) \) will also increase without bound. Hence, the range of \( v(s) \) starts from 10 and goes to infinity.
- Therefore, the range is \( v \geq 10 \) (all values greater than or equal to 10).
- The statements about the range including values less than 10 or being all real numbers are **incorrect**.
Conclusively, the correct statement is: **The domain (s-values) includes the values \( s \geq 0 \)**.
Marilee is creating a garden in her yard. She needs to put up a fence to keep the animals out of it. She has 40 yards of fencing she can erect. This situation is modeled using the equation A=−w^2+20w
, where A
is the area of the fence and w is the width of the fence. If you were to set up a table to determine the measurements of the width and its corresponding area, what would be a reasonable scale for the domain?(1 point)
Responses
5
5 - no response given
1
1 - no response given
2
2 - incorrect
10
, where A
is the area of the fence and w is the width of the fence. If you were to set up a table to determine the measurements of the width and its corresponding area, what would be a reasonable scale for the domain?(1 point)
Responses
5
5 - no response given
1
1 - no response given
2
2 - incorrect
10
GPT-4o mini
To set up a table for the domain using the width \( w \) in the equation \( A = -w^2 + 20w \), we need to determine sensible values for \( w \) based on the fencing constraint and the nature of the quadratic function.
1. **Understanding the equation**:
- The equation is a downward-facing parabola, which describes a maximum area that can be achieved.
- Since the total perimeter is 40 yards of fencing, we have the relationship for a rectangular garden \( P = 2l + 2w = 40 \).
2. **Finding the maximum width**:
- If we rearrange the perimeter equation, we can express the length in terms of the width:
\[
l = 20 - w
\]
- Thus, the width \( w \) must be positive, and the maximum width can be found by setting up bounds.
- Since the width cannot exceed half the total perimeter (20 yards), valid values for \( w \) must be between \( 0 \) and \( 20 \).
3. **Choosing a reasonable scale for the domain**:
- Given that valid values for \( w \) range from \( 0 \) to \( 20 \), a scale of \( 1 \) or \( 5 \) would provide useful measurements for \( w \) to observe the function's properties effectively.
- Using a scale of \( 2 \) would yield fewer data points, making it less practical for detailed analysis. A scale of \( 10 \) would provide even fewer points.
Given these considerations, either a scale of **1** or **5** would be reasonable for the domain. Since you are looking for which option stands out, a scale of **5** would be an effective way to present the width in wider intervals while still producing relevant area calculations.
Thus, if the intention is to pick one answer, **5** is a reasonable scale for the domain.
1. **Understanding the equation**:
- The equation is a downward-facing parabola, which describes a maximum area that can be achieved.
- Since the total perimeter is 40 yards of fencing, we have the relationship for a rectangular garden \( P = 2l + 2w = 40 \).
2. **Finding the maximum width**:
- If we rearrange the perimeter equation, we can express the length in terms of the width:
\[
l = 20 - w
\]
- Thus, the width \( w \) must be positive, and the maximum width can be found by setting up bounds.
- Since the width cannot exceed half the total perimeter (20 yards), valid values for \( w \) must be between \( 0 \) and \( 20 \).
3. **Choosing a reasonable scale for the domain**:
- Given that valid values for \( w \) range from \( 0 \) to \( 20 \), a scale of \( 1 \) or \( 5 \) would provide useful measurements for \( w \) to observe the function's properties effectively.
- Using a scale of \( 2 \) would yield fewer data points, making it less practical for detailed analysis. A scale of \( 10 \) would provide even fewer points.
Given these considerations, either a scale of **1** or **5** would be reasonable for the domain. Since you are looking for which option stands out, a scale of **5** would be an effective way to present the width in wider intervals while still producing relevant area calculations.
Thus, if the intention is to pick one answer, **5** is a reasonable scale for the domain.