Exercise 26 Page 144

Let's first determine the type of function that best describes the number of visitors to the Web site, and then use the general form of it to write a function.

Determining Type of Function

To determine the type of function that best describes the number of visitors to the Web site, we start by finding the differences of successive y-values, namely the first differences.

We see that the first differences are not constant meaning the table does not represents a linear function. Let's find the second difference and compare them.

The second differences are all equal meaning the table represents a quadratic function.

Writing Function

A quadratic equation has the form y=ax^2. For our model, x is time in days and y is the number of visitors in thousands. We can find the value of a by substituting an ordered pair from the table. Let's substitute (1,0.9).

y=ax^2

SubstituteII

x= 1, y= 0.9

0.9=a( 1)^2

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Solve for a

BaseOne

1^a=1

0.9=a(1)

IdPropMult

Identity Property of Multiplication

0.9=a

RearrangeEqn

Rearrange equation

a=0.9

Let's replace a with 0.9. y=ax^2 ⇔ y=0.9x^2 This function models the data.