Question

For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

Answer 1

Consider the table provided in the exercise.

An exponential function is represented as:

f(x) = a(b)x

 

The linear function is represented as:

f(x) = mx + b

 

For exponential function common ratio have to be same and similarly for the linear function common difference have to be same, which is tabulated as shown below:

Linear function Common difference	Exponential function Common ratio
10 – 20 = -10	10/20 = 0.5
20 – 40 = -20	20/40 = 0.5
40 – 80 = -40	40/80 = 0.5

 

 Since, the common is ratio 0.5 is same; therefore, the points represent an exponential function. The formula for the exponential function is f(x) = a(b)0.5.

 Since, the common is ratio 0.5 is same; therefore, the points represent an exponential function. The formula for the exponential function is f(x) = a(b)0.5.