Answer:
Option 4
(0, 1), (1, 3), (2, 9), (3, 27) set of ordered pairs could be generated by an exponential function [tex]f(x)=3^x[/tex].
Step-by-step explanation:
Given : Set of ordered pairs could be generated by an exponential function
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
To find : Which set?
Solution :
The general form of an exponential function is [tex]f(x)=ab^x[/tex]
where,
a is the initial amount [tex]a\neq 0[/tex]
b is the rate of change [tex]b>0 , b\neq 1[/tex]
The graph of each exponential function passes through the point (0,a),
As [tex]f(0)=a\cdot b^0=a[/tex]
and [tex]a\neq 0[/tex]
Therefore, Option 1 and 3 are false.
Now, in Option 2 and 4 first point is (0,1)
i.e, [tex]f(0)=a\cdot b^0\Rightarrow a=1[/tex]
Then, The exponential function form is
[tex]f(x)=b^x[/tex]
In Option 2,
Point (1,2)
[tex]2=b^1\Rightarrow, b=2[/tex]
Point (2,5)
[tex]f(x)=2^2\Rightarrow, f(x)=4[/tex]
which is not correct.
Option 2 is false.
Now, In Option 4
Point (1,3)
[tex]3=b^1\Rightarrow, b=3[/tex]
Point (2,9)
[tex]f(x)=3^2\Rightarrow, f(x)=9[/tex] satisfying
Point (3,27)
[tex]f(x)=3^3\Rightarrow, f(x)=27[/tex] satisfying
Option 4 is true.
Therefore, The exponential form is [tex]f(x)=3^x[/tex]
Hence, option 4 is correct.
(0, 1), (1, 3), (2, 9), (3, 27) set of ordered pairs could be generated by an exponential function [tex]f(x)=3^x[/tex].
