Answer:
Please check the explanation.
Step-by-step explanation:
Here are some of the rules using which we can easily figure out the true nature of a function.
Linear Function:
The constant change in x and y
Quadratic Function:
The constant change in x
The constant 2nd differences in y
Exponential Function:
The constant change in x
The constant ratio in y
Determining the nature of function
Given the table
x -3 -2 -1 0 1 2
y 32 16 8 4 2 1
It is clear that there is a constant change in x
i.e. -2-(-3) = 1, -1-(-2) = 1, 0 - (-1) = 1, 1-0 = 1, 2-1 = 1
Also there is a constant ratio in y
16/32 = 1/2, 8/16 = 1/2, 4/8 = 1/2, 2/4=1/2, 1/2 = 1/2
Therefore, the given function is the exponential function.
Determining the equation
We know the exponential function is of the form
y = abˣ
Taking the point (0, 4) and substitute in the function
4 = ab⁰
as b⁰ = 1, so
4 = a(1)
a = 4
substituting the point (1, 2) and a = 4 in the function
y = abˣ
2 = 4b¹
as b¹ = b, so
2 = 4b
b = 2/4
b = 1/2
Now, substituting a = 4, and b = 1/2 in the function
y = abˣ
y = 4(1/2)ˣ
Therefore, the equation of the function is:
