Question
Question 1 A)Create an exponential function to represent a population of 50 insects that is growing at a rate of 7%. Which of the following functions is accurate?(1 point) Responses f(x)=50(1.7)xf(x)=50(1.7)x f left parenthesis x right parenthesis equals 50 left parenthesis 1.7 right parenthesis superscript x baseline f(x)=50(1.07)xf(x)=50(1.07)x f left parenthesis x right parenthesis equals 50 left parenthesis 1.07 right parenthesis superscript x baseline f(x)=50(0.07)xf(x)=50(0.07)x f left parenthesis x right parenthesis equals 50 left parenthesis 0.07 right parenthesis superscript x baseline f(x)=50(0.93)xf(x)=50(0.93)x f left parenthesis x right parenthesis equals 50 left parenthesis 0.93 right parenthesis superscript x baseline Question 2 A) Use the image to answer the question. The function f(x)=3(1.25)xf(x)=3(1.25)x represents the population growth of a swarm of fruit flies. Create a graph modeling the equation, and determine which graph models the situation accurately. (1 point) Responses Option #1 Option #1 Option #3 Option #3 Option #4 Option #4 Option #2 Option #2 Question 3 A) Use the image to answer the question. Which of the following descriptions best interprets the graph? (1 point) Responses The graph indicates that two cells split into four cells after one cycle. Each cell then splits into two cells in every cycle, exponentially increasing the number of cells. The graph indicates that two cells split into four cells after one cycle. Each cell then splits into two cells in every cycle, exponentially increasing the number of cells. The graph indicates that one cell splits into two cells after one cycle. Each cell then splits into four cells in every cycle, exponentially increasing the number of cells. The graph indicates that one cell splits into two cells after one cycle. Each cell then splits into four cells in every cycle, exponentially increasing the number of cells. The graph demonstrates that one cell splits into two cells after one cycle. Each cell then splits into two cells in every cycle, exponentially increasing the number of cells. The graph demonstrates that one cell splits into two cells after one cycle. Each cell then splits into two cells in every cycle, exponentially increasing the number of cells. The graph demonstrates how several cells decay into almost zero cells. The graph demonstrates how several cells decay into almost zero cells. Question 4 A) Use the image to answer the question. The population of which town(s) demonstrates exponential growth? (1 point) Responses both Town A and Town D both Town A and Town D both Town A and Town B both Town A and Town B only Town A only Town A only Town D only Town D Question 5 A) Use the image to answer the question. The graph shows the total number of COVID-19 cases in the UK from February 23 to April 17 in 2020. The dots or stars represent the actual data points, and the line is an exponential fit for the data points. Each value in the x-axis shows days since COVID cases started to be measured in the UK, with “day 1” representing February 23. The y-axis shows the total number of cases per day. Which of the following correctly uses the graph to determine the best estimate for the number of COVID-19 cases in the UK on day 20? (1 point) Responses 12,000 cases 12,000 cases 10,000 cases 10,000 cases 2,000 cases 2,000 cases 15,000 cases 15,000 cases
Answers
GPT-4o mini
Let's tackle each question one by one:
**Question 1 A)**
To represent a population of 50 insects growing at a rate of 7%, we use the exponential growth formula:
\[ f(x) = P_0 \cdot (1 + r)^x \]
where:
- \( P_0 \) = initial population = 50
- \( r \) = growth rate = 0.07 (7%)
Thus, the function can be represented as:
\[ f(x) = 50(1.07)^x \]
The correct response would be: **f(x) = 50(1.07)^x**
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**Question 2 A)**
Without a specific image to reference, I can't determine which graph accurately models the given equation \( f(x) = 3(1.25)^x \). The correct choice would depend on the visual representation of the exponential growth based on the equation.
---
**Question 3 A)**
Again, without an image to analyze, I can’t definitively state which description accurately interprets the graph. However, in general, for exponential growth indicating cell division, one of the descriptions suggesting that a cell splits into two and continues to halving or doubling (depending on the context) could be appropriate.
---
**Question 4 A)**
Without specific images or data for Town A and Town D, I can't accurately determine which town(s) demonstrate exponential growth. We would need to analyze the population growth graphs for both towns to make a conclusion.
---
**Question 5 A)**
Similar to the previous questions, without the actual graph to review, I can't provide an accurate estimate for the number of COVID-19 cases in the UK on day 20. The best estimate would be the one that aligns with the exponential trend observed in the graph over time.
In summary, only Question 1 can be definitively answered based on the provided information. If you can provide specific details from the images or graphs for Questions 2, 3, 4, and 5, I'd be happy to help you interpret those!
**Question 1 A)**
To represent a population of 50 insects growing at a rate of 7%, we use the exponential growth formula:
\[ f(x) = P_0 \cdot (1 + r)^x \]
where:
- \( P_0 \) = initial population = 50
- \( r \) = growth rate = 0.07 (7%)
Thus, the function can be represented as:
\[ f(x) = 50(1.07)^x \]
The correct response would be: **f(x) = 50(1.07)^x**
---
**Question 2 A)**
Without a specific image to reference, I can't determine which graph accurately models the given equation \( f(x) = 3(1.25)^x \). The correct choice would depend on the visual representation of the exponential growth based on the equation.
---
**Question 3 A)**
Again, without an image to analyze, I can’t definitively state which description accurately interprets the graph. However, in general, for exponential growth indicating cell division, one of the descriptions suggesting that a cell splits into two and continues to halving or doubling (depending on the context) could be appropriate.
---
**Question 4 A)**
Without specific images or data for Town A and Town D, I can't accurately determine which town(s) demonstrate exponential growth. We would need to analyze the population growth graphs for both towns to make a conclusion.
---
**Question 5 A)**
Similar to the previous questions, without the actual graph to review, I can't provide an accurate estimate for the number of COVID-19 cases in the UK on day 20. The best estimate would be the one that aligns with the exponential trend observed in the graph over time.
In summary, only Question 1 can be definitively answered based on the provided information. If you can provide specific details from the images or graphs for Questions 2, 3, 4, and 5, I'd be happy to help you interpret those!