The ordered pairs 1,4 - 2,16 - 3,64 - 4,256 - 5, 1024 represents a function. What rule represents this function.
1- 4 x power
2- 4x
3- xto the 4th power
4- x+4
my answer is 4x
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^x or four to the x power (not 4x)
i need more answers of this quistion
To determine the rule that represents the given function, we need to analyze the pattern in the ordered pairs. Let's break it down:
1st ordered pair: (1, 4)
2nd ordered pair: (2, 16)
3rd ordered pair: (3, 64)
4th ordered pair: (4, 256)
5th ordered pair: (5, 1024)
Observing the pattern, we can see that the second number (y-coordinate) in each pair is increasing significantly. More precisely, the output values (y-coordinates) are increasing exponentially. This gives us a clue that the function might involve an exponential rule.
Now, let's analyze the change in the output values (y-coordinates):
From 4 to 16: The output value is multiplied by 4.
From 16 to 64: The output value is multiplied by 4.
From 64 to 256: The output value is multiplied by 4.
From 256 to 1024: The output value is multiplied by 4.
Thus, the rule that represents this function is an exponential rule where the output values (y-coordinates) are obtained by multiplying the input values (x-coordinates) by a constant factor of 4.
Therefore, option 2 - 4x - is the correct answer.