Question
the graph shows the number of game systems sold since 2015. based on this information, which function best models the number of game systems sold in millions x years since 2015?
a y = 21.35(0.70^x
b y=30.5(21.350^x
c y=30.5(1.3)^x
d y=30.5(0.7)^x
a y = 21.35(0.70^x
b y=30.5(21.350^x
c y=30.5(1.3)^x
d y=30.5(0.7)^x
Answers
Answered by
GPT-4o mini
To determine which function best models the number of game systems sold in millions \( y \) years since 2015, we need to analyze the given options based on their forms.
1. **Exponential Growth:** The functions with a base greater than 1 will indicate growth, while bases between 0 and 1 will indicate decay.
2. **Given Options:**
- \( a) \; y = 21.35(0.70^x \) - This represents a decline in sales since the base is 0.70.
- \( b) \; y = 30.5(21.350^x \) - This is unusual since \( 21.350 \) is much greater than 1, indicating extreme growth over time, which is unlikely in this context.
- \( c) \; y = 30.5(1.3)^x \) - This indicates growth, as 1.3 is greater than 1.
- \( d) \; y = 30.5(0.7)^x \) - Similar to option a, this indicates a decline since the base is 0.7.
Given that game system sales typically do not show extreme growth but rather might decline over time, the most realistic options are **a** or **d** if you are looking for models capturing a decline.
To make a final choice between the two options (a and d), more context from the graph is needed, such as whether the trend line suggests an upward trajectory (where option c might be reasonable) or if the sales have been declining.
Without the visual of the graph, based entirely on the options provided and typical sales trends, it would be prudent to lean towards **option a** or **option d**, depending on whether sales have declined modestly or more aggressively.
If the sales trend appears stable or growing, option **c** could also be a contender.
**Conclusion:**
- If sales appear to decline, choose **a** (21.35(0.70^x)) or **d** (30.5(0.7)^x).
- If sales appear to increase, choose **c** (30.5(1.3)^x).
Check the graph for the sales pattern to finalize your choice.
1. **Exponential Growth:** The functions with a base greater than 1 will indicate growth, while bases between 0 and 1 will indicate decay.
2. **Given Options:**
- \( a) \; y = 21.35(0.70^x \) - This represents a decline in sales since the base is 0.70.
- \( b) \; y = 30.5(21.350^x \) - This is unusual since \( 21.350 \) is much greater than 1, indicating extreme growth over time, which is unlikely in this context.
- \( c) \; y = 30.5(1.3)^x \) - This indicates growth, as 1.3 is greater than 1.
- \( d) \; y = 30.5(0.7)^x \) - Similar to option a, this indicates a decline since the base is 0.7.
Given that game system sales typically do not show extreme growth but rather might decline over time, the most realistic options are **a** or **d** if you are looking for models capturing a decline.
To make a final choice between the two options (a and d), more context from the graph is needed, such as whether the trend line suggests an upward trajectory (where option c might be reasonable) or if the sales have been declining.
Without the visual of the graph, based entirely on the options provided and typical sales trends, it would be prudent to lean towards **option a** or **option d**, depending on whether sales have declined modestly or more aggressively.
If the sales trend appears stable or growing, option **c** could also be a contender.
**Conclusion:**
- If sales appear to decline, choose **a** (21.35(0.70^x)) or **d** (30.5(0.7)^x).
- If sales appear to increase, choose **c** (30.5(1.3)^x).
Check the graph for the sales pattern to finalize your choice.