Does the table represent an exponential function?
x | 1 | 2 | 3 | 4
y | -2 | -12 | -72 | -432
What do you mean?
To determine if the table represents an exponential function, we need to check if there is a common ratio between the y-values as the x-values increase by a constant amount.
Let's calculate the ratio between consecutive y-values:
Ratio between y-values:
-12 / -2 = 6
-72 / -12 = 6
-432 / -72 = 6
The ratio between consecutive y-values in the table is 6. Since there is a constant ratio, we can conclude that the table represents an exponential function.
To determine if the table represents an exponential function, we need to check if there is a constant ratio between the y-values for each of the corresponding x-values.
Let's calculate the ratios between the consecutive y-values and see if they are the same:
-12 / -2 = 6
-72 / -12 = 6
-432 / -72 = 6
Since the ratios between the y-values are the same (6), this table represents an exponential function.
To clarify the calculation process again, you divide the y-value of one row by the y-value of the previous row in the table. If the ratios between all consecutive y-values are the same, then it represents an exponential function.
Factor out the -2 everywhere.
What do you see?