Question
Y=-3(4)[^x+3]+2 arrow y=-6(4)^[x+6]+4
Answers
GPT-4o mini
Let's analyze the expression step by step.
You have the equation:
\[ y = -3(4)^{-x + 3} + 2 \]
We want to rewrite it in the form of:
\[ y = -6(4)^{x + 6} + 4 \]
To check if the two expressions are equivalent, we can simplify the first one and see if it leads us to the second expression.
1. **Rewrite the first equation**:
Start with:
\[ y = -3 \cdot 4^{-x + 3} + 2 \]
We can rewrite \( 4^{-x + 3} \) as \( 4^3 \cdot 4^{-x} = 64 \cdot 4^{-x} \). So,
\[ y = -3 \cdot (64 \cdot 4^{-x}) + 2 \]
\[ y = -192 \cdot 4^{-x} + 2 \]
2. **Rearranging**:
Rearranging gives:
\[ y = -192 (4^{-x}) + 2 \]
3. **Factor out constants**:
We can factor out constants for comparison. The expression needs to be rewritten as a multiples of powers of 4.
Assuming \( 4^{-x} = \frac{1}{4^x} \), our equation becomes:
\[ y = -192 \cdot \frac{1}{4^x} + 2 \]
4. **Making equivalent transformation**:
Notice that any term can be transformed to compare if needed. However, there does not seem to be a direct transformation between a negative leading term in the first equation becoming a positive in the second without modification.
5. **Conclusion**:
The two equations provided do not seem to represent the same mathematical expression in their current form. To determine if they can be related would require additional transformations or justification, such as behavior or origin methods.
If you need a transformation in another specific way or need to see if they can be equivalent through any constraints, please specify!
You have the equation:
\[ y = -3(4)^{-x + 3} + 2 \]
We want to rewrite it in the form of:
\[ y = -6(4)^{x + 6} + 4 \]
To check if the two expressions are equivalent, we can simplify the first one and see if it leads us to the second expression.
1. **Rewrite the first equation**:
Start with:
\[ y = -3 \cdot 4^{-x + 3} + 2 \]
We can rewrite \( 4^{-x + 3} \) as \( 4^3 \cdot 4^{-x} = 64 \cdot 4^{-x} \). So,
\[ y = -3 \cdot (64 \cdot 4^{-x}) + 2 \]
\[ y = -192 \cdot 4^{-x} + 2 \]
2. **Rearranging**:
Rearranging gives:
\[ y = -192 (4^{-x}) + 2 \]
3. **Factor out constants**:
We can factor out constants for comparison. The expression needs to be rewritten as a multiples of powers of 4.
Assuming \( 4^{-x} = \frac{1}{4^x} \), our equation becomes:
\[ y = -192 \cdot \frac{1}{4^x} + 2 \]
4. **Making equivalent transformation**:
Notice that any term can be transformed to compare if needed. However, there does not seem to be a direct transformation between a negative leading term in the first equation becoming a positive in the second without modification.
5. **Conclusion**:
The two equations provided do not seem to represent the same mathematical expression in their current form. To determine if they can be related would require additional transformations or justification, such as behavior or origin methods.
If you need a transformation in another specific way or need to see if they can be equivalent through any constraints, please specify!