Question

find five ordered pairs for each function. make a table of values.

1. ( y = 5^x )

substitute:
0 for ( x )
1 for ( x )
2 for ( x )
3 for ( x )
4 for ( x )
(0, ■), (1, ■), (2, ■), (3, ■), and (■, ■) are five ordered pairs for ( y = 5^x ).

1. ( y = 4 cdot 2^x )

substitute:
0 for ( x )
1 for ( x )
2 for ( x )
3 for ( x )
4 for ( x )
(0, ■), (1, ■), (2, ■), (3, ■), and (■, ■) are five ordered pairs for ( y = 4 cdot 2^x ).

practice
find five ordered pairs for each function. make a table of values. begin with ( x = 0 ).

1. ( y = 4^x )
2. ( y = 3^x )
3. ( y = -2 cdot 5^x )

find four ordered pairs for each function. make a table of values. begin with ( x = 0 ).

1. ( y = 10^x )
2. ( y = 8^x )
3. ( y = 20^x )

Explanation:

Problem 1: \( y = 5^x \)

Step1: Substitute \( x = 0 \)

\( y = 5^0 = 1 \)

Step2: Substitute \( x = 1 \)

\( y = 5^1 = 5 \)

Step3: Substitute \( x = 2 \)

\( y = 5^2 = 25 \)

Step4: Substitute \( x = 3 \)

\( y = 5^3 = 125 \)

Step5: Substitute \( x = 4 \)

\( y = 5^4 = 625 \)

Step1: Substitute \( x = 0 \)

\( y = 4 \cdot 2^0 = 4 \cdot 1 = 4 \)

Step2: Substitute \( x = 1 \)

\( y = 4 \cdot 2^1 = 4 \cdot 2 = 8 \)

Step3: Substitute \( x = 2 \)

\( y = 4 \cdot 2^2 = 4 \cdot 4 = 16 \)

Step4: Substitute \( x = 3 \)

\( y = 4 \cdot 2^3 = 4 \cdot 8 = 32 \)

Step5: Substitute \( x = 4 \)

\( y = 4 \cdot 2^4 = 4 \cdot 16 = 64 \)

Step1: Substitute \( x = 0 \)

\( y = 4^0 = 1 \)

Step2: Substitute \( x = 1 \)

\( y = 4^1 = 4 \)

Step3: Substitute \( x = 2 \)

\( y = 4^2 = 16 \)

Step4: Substitute \( x = 3 \)

\( y = 4^3 = 64 \)

Step5: Substitute \( x = 4 \)

\( y = 4^4 = 256 \)

Answer:

The five ordered pairs are \((0, 1)\), \((1, 5)\), \((2, 25)\), \((3, 125)\), and \((4, 625)\)

Problem 2: \( y = 4 \cdot 2^x \)