Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine which exponential function is represented by the table, we need to analyze the table values for [tex]\( f(x) \)[/tex] for given [tex]\( x \)[/tex].
The table is given as:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -2 & 12.5 \\ -1 & 2.5 \\ 0 & 0.5 \\ 1 & 0.1 \\ 2 & 0.02 \\ \hline \end{array} \][/tex]
We are given four possible exponential functions to consider:
1. [tex]\( f(x) = 0.2 \left( 0.5^x \right) \)[/tex]
2. [tex]\( f(x) = 0.5 \left( 5^x \right) \)[/tex]
3. [tex]\( f(x) = 0.5 \left ( 0.2^x \right) \)[/tex]
4. [tex]\( f(x) = 0.2 \left( 0.2^x \right) \)[/tex]
We need to check each function to see which one corresponds with all the values in the table.
1. For [tex]\( f(x) = 0.2 \left( 0.5^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.2 \left( 0.5^{-2} \right) = 0.2 \left( 4 \right) = 0.8 \][/tex]
- The value does not match [tex]\( f(-2) = 12.5 \)[/tex]. So this function is not the correct one.
2. For [tex]\( f(x) = 0.5 \left( 5^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.5 \left( 5^{-2} \right) = 0.5 \left( 0.04 \right) = 0.02 \][/tex]
- This value does not match [tex]\( f(-2) = 12.5 \)[/tex]. Thus, this function is not the correct one.
3. For [tex]\( f(x) = 0.5 \left( 0.2^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.5 \left( 0.2^{-2} \right) = 0.5 \left( 25 \right) = 12.5 \][/tex]
- Calculating for [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 0.5 \left( 0.2^{-1} \right) = 0.5 \left( 5 \right) = 2.5 \][/tex]
- Calculating for [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 0.5 \left( 0.2^{0} \right) = 0.5 \left( 1 \right) = 0.5 \][/tex]
- Calculating for [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 0.5 \left( 0.2^{1} \right) = 0.5 \left( 0.2 \right) = 0.1 \][/tex]
- Calculating for [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 0.5 \left( 0.2^{2} \right) = 0.5 \left( 0.04 \right) = 0.02 \][/tex]
- All these values align perfectly with the given table values. So this function seems to be a match.
4. For [tex]\( f(x) = 0.2 \left( 0.2^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.2 \left( 0.2^{-2} \right) = 0.2 \left( 25 \right) = 5 \][/tex]
- This value does not match [tex]\( f(-2) = 12.5 \)[/tex]. Thus, this function is not correct.
In conclusion, the exponential function that matches the table is:
[tex]\[ f(x) = 0.5 \left( 0.2^x \right) \][/tex]
The table is given as:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -2 & 12.5 \\ -1 & 2.5 \\ 0 & 0.5 \\ 1 & 0.1 \\ 2 & 0.02 \\ \hline \end{array} \][/tex]
We are given four possible exponential functions to consider:
1. [tex]\( f(x) = 0.2 \left( 0.5^x \right) \)[/tex]
2. [tex]\( f(x) = 0.5 \left( 5^x \right) \)[/tex]
3. [tex]\( f(x) = 0.5 \left ( 0.2^x \right) \)[/tex]
4. [tex]\( f(x) = 0.2 \left( 0.2^x \right) \)[/tex]
We need to check each function to see which one corresponds with all the values in the table.
1. For [tex]\( f(x) = 0.2 \left( 0.5^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.2 \left( 0.5^{-2} \right) = 0.2 \left( 4 \right) = 0.8 \][/tex]
- The value does not match [tex]\( f(-2) = 12.5 \)[/tex]. So this function is not the correct one.
2. For [tex]\( f(x) = 0.5 \left( 5^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.5 \left( 5^{-2} \right) = 0.5 \left( 0.04 \right) = 0.02 \][/tex]
- This value does not match [tex]\( f(-2) = 12.5 \)[/tex]. Thus, this function is not the correct one.
3. For [tex]\( f(x) = 0.5 \left( 0.2^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.5 \left( 0.2^{-2} \right) = 0.5 \left( 25 \right) = 12.5 \][/tex]
- Calculating for [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 0.5 \left( 0.2^{-1} \right) = 0.5 \left( 5 \right) = 2.5 \][/tex]
- Calculating for [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 0.5 \left( 0.2^{0} \right) = 0.5 \left( 1 \right) = 0.5 \][/tex]
- Calculating for [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 0.5 \left( 0.2^{1} \right) = 0.5 \left( 0.2 \right) = 0.1 \][/tex]
- Calculating for [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 0.5 \left( 0.2^{2} \right) = 0.5 \left( 0.04 \right) = 0.02 \][/tex]
- All these values align perfectly with the given table values. So this function seems to be a match.
4. For [tex]\( f(x) = 0.2 \left( 0.2^x \right) \)[/tex]:
- Calculating for [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 0.2 \left( 0.2^{-2} \right) = 0.2 \left( 25 \right) = 5 \][/tex]
- This value does not match [tex]\( f(-2) = 12.5 \)[/tex]. Thus, this function is not correct.
In conclusion, the exponential function that matches the table is:
[tex]\[ f(x) = 0.5 \left( 0.2^x \right) \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
