Answer:
The given table form an exponential function
.
Explanation:
Given : Table
x 0 1 2 3 4
f(x) 10 20 40 80 160
To find : Determine the appropriate model of the function?
Solution :
To determine we find the difference of the given function as
- If the first difference is the same value, the model will be linear.
- If the second difference is the same value, the model will be quadratic.
- If the number of times the difference has been taken before finding repeated values, the model may be exponential or some other special equation.
Now, we find the difference
20-10=10
40-20=20
80-40=40
160-80=80
The difference were not equal so the given function is an exponential function as it satisfy the condition of exponential form.

We find a and b by substituting the value of x and y
When, x=0 and y=10


When, x=1 and y=20



So, The exponential form is

Verification



So, at x=3 y is 80.
Therefore, The given table form an exponential function
.