Question
Chen is given the graph below.
mc024-1.jpg
What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
mc024-1.jpg
What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
Answers
GPT-4o mini
To determine what type of graph is shown and its growth factor, we typically look at the characteristics of the graph.
1. **Linear function**: A linear function has a constant rate of change and appears as a straight line. The growth factor for a linear function is not typically described in the same way as exponential growth.
2. **Exponential function**: An exponential function grows at a rate proportional to its current value, resulting in a curve that increases rapidly. The growth factor indicates how much the value increases for each unit increase in the independent variable (often time).
If the graph appears as a straight line, it would be a linear function. If it curves upwards rapidly, it would be an exponential function.
- If the graph is an exponential function that doubles (for example, each time \(x\) increases by 1, \(y\) doubles), it would have a growth factor of 2.
- If the function quadruples (for example, each time \(x\) increases by 1, \(y\) quadruples), it would have a growth factor of 4.
Without the visual context of the graph, I can only provide the analysis based on common knowledge. Based on that, if the graph is clearly exponential and shows a doubling effect, then it would be "exponential function; growth factor of 2". If it is a doubling most closely related to a square or quadrupling effect, it would be "exponential function; growth factor of 4."
Thus, if you see that the values are consistently doubling, choose "exponential function; growth factor of 2." If they're quadrupling, choose "exponential function; growth factor of 4." If it's linear, the first two options wouldn't apply.
Please refer to the graph to finalize the answer.
1. **Linear function**: A linear function has a constant rate of change and appears as a straight line. The growth factor for a linear function is not typically described in the same way as exponential growth.
2. **Exponential function**: An exponential function grows at a rate proportional to its current value, resulting in a curve that increases rapidly. The growth factor indicates how much the value increases for each unit increase in the independent variable (often time).
If the graph appears as a straight line, it would be a linear function. If it curves upwards rapidly, it would be an exponential function.
- If the graph is an exponential function that doubles (for example, each time \(x\) increases by 1, \(y\) doubles), it would have a growth factor of 2.
- If the function quadruples (for example, each time \(x\) increases by 1, \(y\) quadruples), it would have a growth factor of 4.
Without the visual context of the graph, I can only provide the analysis based on common knowledge. Based on that, if the graph is clearly exponential and shows a doubling effect, then it would be "exponential function; growth factor of 2". If it is a doubling most closely related to a square or quadrupling effect, it would be "exponential function; growth factor of 4."
Thus, if you see that the values are consistently doubling, choose "exponential function; growth factor of 2." If they're quadrupling, choose "exponential function; growth factor of 4." If it's linear, the first two options wouldn't apply.
Please refer to the graph to finalize the answer.