Respuesta :
Answer:
The correct option is B.
Step-by-step explanation:
A function is called an exponential function if it has common ratio.
A function is called an linear function if it has common difference.
In option A.
[tex]\frac{f(2)}{f(1)}=\frac{6}{3}=2[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
[tex]2\neq \frac{3}{2}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option A is incorrect.
In option B.
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=3[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=3[/tex]
[tex]3=3[/tex]
Since the given table has common ratio, therefore it is an exponential function. Option B is correct.
In option C.
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
[tex]\frac{11}{5}\neq \frac{17}{11}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option C is incorrect.
In option D.
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
[tex]\frac{8}{7}\neq \frac{9}{8}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option D is incorrect.
Answer:
Table B represents an exponential function.
Step-by-step explanation:
An exponential function is a function which has common ratio. Using this fact we will evaluate the functions given in the form of a table.
Table A.
f(1) = 3
f(2) = 6
f(3) = 9
Now [tex]\frac{f(2)}{f(1)}=\frac{6}{3}=\frac{2}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
Ratios are not equal so it's not an exponential function.
Table B.
f(1) = 2
f(2) = 6
f(3) = 18
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=\frac{3}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=\frac{3}{1}[/tex]
Here ratios are same therefore it's an exponential function.
Table C.
f(1) = 10
f(2) = 22
f(3) = 34
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
Ratios are not equal therefore it's not an exponential function.
Table D.
f(1) = 7
f(2) = 8
f(3) = 9
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
Ratios are not equal so it's not an exponential function.
Therefore Table B is the correct option.
