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The table of ordered pairs (x, y) gives an exponential function. Write an equation for the function. X 7 0 1 a y 1 20 1 5 50

The table of ordered pairs (x, y) gives an exponential function. Write an equation for the function. X 7 0 1 a y 1 20 1 5 50

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Writing an Exponential Function Rule Given a Table of Ordered Pairs** The table of ordered pairs \((x, y)\) gives an exponential function. Write an equation for the function. | \(x\) | \(y\) | |-------|-----------| | \(-1\) | \(\frac{1}{20}\) | | \(0\) | \(\frac{1}{2}\) | | \(1\) | \(5\) | | \(2\) | \(50\) | To determine the exponential function, observe the relationship between the \(x\) and \(y\) values. The steps typically involve recognizing the base and initial value from the table and using it to form the equation \(y = a \cdot b^x\), where \(a\) is the initial value and \(b\) is the base or growth factor. The image also contains graphical elements that appear to be placeholders or icons, but lack details for further explanation.
Transcribed Image Text:**Writing an Exponential Function Rule Given a Table of Ordered Pairs** The table of ordered pairs \((x, y)\) gives an exponential function. Write an equation for the function. | \(x\) | \(y\) | |-------|-----------| | \(-1\) | \(\frac{1}{20}\) | | \(0\) | \(\frac{1}{2}\) | | \(1\) | \(5\) | | \(2\) | \(50\) | To determine the exponential function, observe the relationship between the \(x\) and \(y\) values. The steps typically involve recognizing the base and initial value from the table and using it to form the equation \(y = a \cdot b^x\), where \(a\) is the initial value and \(b\) is the base or growth factor. The image also contains graphical elements that appear to be placeholders or icons, but lack details for further explanation.
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