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Algebra
Question

The graphs labeled (a)-(d) in the figure represent...

The graphs labeled (a)-(d) in the figure represent \(y = 3 ^ { x }\) ,\(y = 5 ^ { x } , y = ( \frac { 1 } { 3 } ) ^ { x } ,\) and \(y = ( \frac { 1 } { 5 } ) ^ { x }\) , but not necessarily in that order. Which is which? Describe the process that justifies this decision. The graph labeled (a) represents the graph of \(y = ( \frac { 1 } { 3 } ) ^ { x }\) , the graph labeled (b) represents the graph of \(y = ( \frac { 1 } { 5 } ) ^ { x }\),the graph labeled (c) represents the graph of \(\quad y = 5 ^ { x } , \quad\) and the graph labeled (d) represents the graph of \(y = 3 ^ { x }\) .

The exponential functions with base \(\square 1\) are increasing functions. The function \(\square\)increases more rapidly than \(\square\) The exponential functions with base \(\square\) 1 are decreasing functions. The function \(\square\) decreases more rapidly than \(\square\)

Answer

greater than 

\(y= 5^{x}\)         \(y= 3^{x}\)

less than

\(y= (\frac{1}{5} )^x\)     \(y= (\frac{1}{3} )^x\)

Solution
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