Question

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.

Answer 1

Option a is correct

given data in the table represents an exponential function

The possible formula for the function is,
`y = f(x) = 12.5 (1.10)^x`

An exponential function is in the form of
`f(x) = ab^x` where a is the initial value and b ≠ 0 , b> 1.

Consider any two points from the table as shown;

(0, 12.5) and (1, 13.75)

Substitute these in [1] we have;

For (0, 12.5)

where x = 0 and f(x) = 12.5 in [1]

`12.5 = ab^0`

12.5 = a

For (1, 13.75)

`13.75 = ab^1`

13.75 = ab

Substitute the value of a =12.5 we have;

13.75 = 12.5b

divide both sides by 12.5 we get;

`b = (13.75)/(12.5) = 1.10`

since, y =f(x)

therefore, we have the following exponential function as:

`y= 12.5 (1.10)^x`