Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Consider the table representing an exponential function. The equation for this function is:

[tex]\[
\begin{tabular}{|r|r|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-2 & 32 \\
\hline
-1 & 16 \\
\hline
0 & 8 \\
\hline
1 & 4 \\
\hline
2 & 2 \\
\hline
3 & 1 \\
\hline
\end{tabular}
\][/tex]

[tex]\[ f(x) = \square (\square)^x \][/tex]

(Note: The placeholders [tex]\(\square\)[/tex] indicate where you need to fill in the coefficients and base for the exponential function.)

Sagot :

GinnyAnswer
To determine the equation of the exponential function \( f(x) \) from the given table, we need to identify the form of the exponential function:

[tex]\[ f(x) = A \cdot B^x \][/tex]

Here, \( A \) and \( B \) are constants we need to find. The table of values given is:

[tex]\[ \begin{array}{|r|r|} \hline x & f(x) \\ \hline -2 & 32 \\ \hline -1 & 16 \\ \hline 0 & 8 \\ \hline 1 & 4 \\ \hline 2 & 2 \\ \hline 3 & 1 \\ \hline \end{array} \][/tex]

Let's find \( A \) and \( B \) step-by-step:

1. Finding \( A \):
The value \( A \) can be found by looking at \( f(0) \):

[tex]\[ f(0) = A \cdot B^0 = A \][/tex]

Given \( f(0) = 8 \):

[tex]\[ A = 8 \][/tex]

2. Finding \( B \):
Next, we use two consecutive points from the table to determine \( B \). Let's use \( x = 1 \) and \( x = 0 \) for simplicity:

[tex]\[ f(1) = A \cdot B^1 = 8 \cdot B \][/tex]

Given \( f(1) = 4 \):

[tex]\[ 8 \cdot B = 4 \][/tex]

Solving for \( B \):

[tex]\[ B = \frac{4}{8} = 0.5 \][/tex]

Putting these values of \( A \) and \( B \) together, the equation for the exponential function is:

[tex]\[ f(x) = 8 \cdot (0.5)^x \][/tex]

Therefore, the complete function is:

[tex]\[ f(x) = 8 \cdot 0.5^x \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.