Questions: Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or linear, find a function that passes through the points. If the function is neither exponential nor linear, type 'NONE'. (If exponential, write the form f(x)=a b^x, if linear, write the form f(x)=m x+b ) x 1 2 3 4 f(x) 70 49 34.3 24.01 f(x)=

Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or linear, find a function that passes through the points. If the function is neither exponential nor linear, type 'NONE'. (If exponential, write the form f(x)=a b^x, if linear, write the form f(x)=m x+b )

x 1 2 3 4 
f(x) 70 49 34.3 24.01 

f(x)=
Transcript text: Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or linear, find a function that passes through the points. If the function is neither exponential nor linear, type 'NONE'. (If exponential, write the form $f(x)=a b^{x}$, if linear, write the form $f(x)=m x+b$ ) \begin{tabular}{|c|c|c|c|c|} \hline$x$ & 1 & 2 & 3 & 4 \\ \hline$f(x)$ & 70 & 49 & 34.3 & 24.01 \\ \hline \end{tabular} $f(x)=\square$
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Solution

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Solution Steps

Step 1: Exponential Check

Calculated constant ratio for exponential function: \(b = 0.7\) Using the point \((1, 70)\), calculated \(a = 100\)

Final Answer:

The function is exponential with \(f(x) = 100 * 0.7^{x}\).

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