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

Option a is correct

given data in the table represents an exponential function

The possible formula for the function is,

An exponential function is in the form of 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 = a

For (1, 13.75)

13.75 = ab

Substitute the value of a =12.5 we have;

13.75 = 12.5b

divide both sides by 12.5 we get;

since, y =f(x)

therefore, we have the following exponential function as:

ANSWER:  

The 75% of 400 is 300.

SOLUTION:

Given, 75% of 400.  

We have to Write and evaluate an expression to find the answer. Then we have explain how to use the model to justify the answer.

Now, let x and y be any two numbers such that, 0 ≤ y ≤ 100

Now, let us substitute the given values in above expression.

We have to do the same procedure for any given values.

Hence, the 75% of 400 is 300.