Question

The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.

x l y
-----------
-1 2
0 8
1 32
2 128

Answer 1

Given :   The table of ordered pairs (x, y) gives an exponential function.

x l y

-----------

-1 2

0 8

1 32

2 128

To find :  an equation for the function.

Solution:

all terms of y  are  powers of 2

Lets assume  function is

$y = 2^{(ax + b)}$

y = 2⁽ᵃˣ⁺ᵇ)

x = - 1     y  = 2 = 2¹

=> ax + b = 1   =>  -a  + b = 1

=> b  -a  = 1

x = 0     y  = 8 = 2³

=> ax + b = 3   =>  0  + b = 3

=> b   =  3

b -a  = 1

=> 3  - a  = 1

=> a = 2

Lets check others

x  = 1    y  = 32 = 2⁵

ax + b = 2(1)  +  3  = 5

x = 2    y = 128  = 2⁷

ax + b = 2(2) + 3 = 7

all satisfied

Hence   y  = 2⁽²ˣ ⁺³⁾  

  $y = 2^{(2x + 3)}$

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