Math  /  Algebra

QuestionThe following table represents an exponential function. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 0 & 4 \\ \hline 1 & 2 \\ \hline 2 & 1 \\ \hline 3 & 12\frac{1}{2} \\ \hline 4 & 14\frac{1}{4} \\ \hline \end{tabular}
The exponential function represented by the table can be written in the form y=abxy=a b^{x}. Find the values for aa and bb. a=a=\square b=b= \square

Studdy Solution
Verify the values of a a and b b using additional points. Check x=2 x = 2 , where y=1 y = 1 : y=ab2=4(12)2=4×14=1 y = a b^2 = 4 \left(\frac{1}{2}\right)^2 = 4 \times \frac{1}{4} = 1
The values are consistent with the table, confirming a=4 a = 4 and b=12 b = \frac{1}{2} .
The exponential function is: a=4 a = 4 b=12 b = \frac{1}{2}

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