The table represents some points on the graph of an exponential function.
- 1
k (x)
0.02
1
3
2
200
5
20,000
Based on the table, which function represents the same relationship?
Let's analyze the table and look for patterns.
For an exponential function, as x increases, the value of y also increases exponentially.
Looking at the points, we can see that as x increases, the value of y increases significantly:
k(1) = 0.02
k(3) = 2
k(5) = 20,000
This rapid increase suggests that the function is growing exponentially.
Additionally, when x = -1, we have k(-1) = -1, which is a negative value. This suggests that the function reflects or moves below the x-axis.
Based on these observations, we can conclude that the function that represents the same relationship is an exponential function that is reflected or moves below the x-axis.
Therefore, one possible function is:
k(x) = -a^x, where a > 1
Note: The specific value of "a" cannot be determined with the given table.