Question
The graph shows the number of game consoles sold in millions since 2009.
Based on this information, which function best models the number of game consoles sold in millions x
years since 2009?
(1 point)
Responses
g(x)=0.6(25.5)x
g of x is equal to 0 point 6 times 25 point 5 to the x th power
g(x)=25.5(0.6)x
g of x is equal to 25 point 5 times 0 point 6 to the x th power
g(x)=6.12(25.5)x
g of x is equal to 6 point 1 2 times 25 point 5 to the x th power
g(x)=25.5(6.12)x
Based on this information, which function best models the number of game consoles sold in millions x
years since 2009?
(1 point)
Responses
g(x)=0.6(25.5)x
g of x is equal to 0 point 6 times 25 point 5 to the x th power
g(x)=25.5(0.6)x
g of x is equal to 25 point 5 times 0 point 6 to the x th power
g(x)=6.12(25.5)x
g of x is equal to 6 point 1 2 times 25 point 5 to the x th power
g(x)=25.5(6.12)x
Answers
Answered by
GPT-4o mini
To determine which function best models the number of game consoles sold in millions \( g(x) \) as a function of years since 2009:
1. **Understanding the Formats:**
- The functions given are of the form \( g(x) = a \cdot b^x \), where:
- \( a \) represents the initial quantity (when \( x = 0 \), in this case, 2009).
- \( b \) is the growth factor indicating how the quantity changes over time.
2. **Examine the Options:**
- **a)** \( g(x) = 0.6(25.5)^x \)
- **b)** \( g(x) = 25.5(0.6)^x \)
- **c)** \( g(x) = 6.12(25.5)^x \)
- **d)** \( g(x) = 25.5(6.12)^x \)
3. **Evaluating Each Function:**
- **Option a)** starts at 0.6 million and appears to grow exponentially with a base of 25.5, which is likely unrealistic for initial sales data.
- **Option b)** starts with 25.5 million and decreases over time, implying sales are declining, which may not fit the trends of game console sales in later years.
- **Option c)** starts at 6.12 million and grows exponentially with 25.5, suggesting initial sales growth.
- **Option d)** starts at 25.5 million but with a diminishing growth factor of 6.12, suggesting significant initial sales but lower growth.
4. **Contextual Relevance:**
- Game console sales typically show an initial spike followed by either growth/plateau or a decline in growth. The model should reflect initial higher sales and then adjust depending on market trends.
Based on this analysis, without specific graph data, the best choice among the options provided—assuming a more typical growth pattern seen with technology products—would likely be:
**\( g(x) = 6.12(25.5)^x \)** (option c), as it implies a positive growth starting from a reasonable initial estimate while growing exponentially.
1. **Understanding the Formats:**
- The functions given are of the form \( g(x) = a \cdot b^x \), where:
- \( a \) represents the initial quantity (when \( x = 0 \), in this case, 2009).
- \( b \) is the growth factor indicating how the quantity changes over time.
2. **Examine the Options:**
- **a)** \( g(x) = 0.6(25.5)^x \)
- **b)** \( g(x) = 25.5(0.6)^x \)
- **c)** \( g(x) = 6.12(25.5)^x \)
- **d)** \( g(x) = 25.5(6.12)^x \)
3. **Evaluating Each Function:**
- **Option a)** starts at 0.6 million and appears to grow exponentially with a base of 25.5, which is likely unrealistic for initial sales data.
- **Option b)** starts with 25.5 million and decreases over time, implying sales are declining, which may not fit the trends of game console sales in later years.
- **Option c)** starts at 6.12 million and grows exponentially with 25.5, suggesting initial sales growth.
- **Option d)** starts at 25.5 million but with a diminishing growth factor of 6.12, suggesting significant initial sales but lower growth.
4. **Contextual Relevance:**
- Game console sales typically show an initial spike followed by either growth/plateau or a decline in growth. The model should reflect initial higher sales and then adjust depending on market trends.
Based on this analysis, without specific graph data, the best choice among the options provided—assuming a more typical growth pattern seen with technology products—would likely be:
**\( g(x) = 6.12(25.5)^x \)** (option c), as it implies a positive growth starting from a reasonable initial estimate while growing exponentially.