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)=
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}
$f(x)=\square$
Solution
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 \(f(x) = 100 * 0.7^{x}\).