Question
Given the graph of the exponential equation, write the correct exponential equation for the graph.
(1 point)
Responses
y=32(3)x
y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline
y=2(3/2)x
y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline
y=3(2/3)x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline
y=3(3/2)x
(1 point)
Responses
y=32(3)x
y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline
y=2(3/2)x
y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline
y=3(2/3)x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline
y=3(3/2)x
Answers
Answered by
GPT-4o mini
To determine the correct exponential equation for the graph, we need to find key characteristics such as the initial value (the y-intercept when x=0) and the growth (or decay) factor (the base of the exponent).
Without the actual graph, I can only provide you with a guideline on how to select the correct equation based on common characteristics of exponential functions.
1. **Identify Initial Value**: Look at the y-coordinate when x = 0. This will give you the initial value (the coefficient in front of the exponential part).
2. **Identify Growth/Decay Factor**: Determine how quickly the function increases or decreases as x changes. If values rise quickly, it's likely a growth function, and the base will be greater than 1. If values decrease, the base will be between 0 and 1.
Once you have that information, compare it with the provided options:
- If the initial value is **32** and the growth factor is **3**, it would be **y = 32(3)^x**.
- If the function starts at **3/2** and grows by a factor of **3/2**, it would be **y = (3/2)(3)^x**.
- If it starts at **2** and grows by a factor of **3/2**, it would fit **y = 2(3/2)^x**.
- If it starts at **3** and decays (or grows) by a factor of **2/3**, it matches **y = 3(2/3)^x**.
- If it starts at **3** and grows by **3/2**, it matches **y = 3(3/2)^x**.
Select the equation that reflects the initial value and growth/decay behavior as seen in your graph. If you want to provide more details about the graph's behavior, I can help narrow it down further!
Without the actual graph, I can only provide you with a guideline on how to select the correct equation based on common characteristics of exponential functions.
1. **Identify Initial Value**: Look at the y-coordinate when x = 0. This will give you the initial value (the coefficient in front of the exponential part).
2. **Identify Growth/Decay Factor**: Determine how quickly the function increases or decreases as x changes. If values rise quickly, it's likely a growth function, and the base will be greater than 1. If values decrease, the base will be between 0 and 1.
Once you have that information, compare it with the provided options:
- If the initial value is **32** and the growth factor is **3**, it would be **y = 32(3)^x**.
- If the function starts at **3/2** and grows by a factor of **3/2**, it would be **y = (3/2)(3)^x**.
- If it starts at **2** and grows by a factor of **3/2**, it would fit **y = 2(3/2)^x**.
- If it starts at **3** and decays (or grows) by a factor of **2/3**, it matches **y = 3(2/3)^x**.
- If it starts at **3** and grows by **3/2**, it matches **y = 3(3/2)^x**.
Select the equation that reflects the initial value and growth/decay behavior as seen in your graph. If you want to provide more details about the graph's behavior, I can help narrow it down further!