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Big Ideas Math Algebra 2, 2014

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Big Ideas Math Algebra 2, 2014 View details

Mathematical Practices

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Exercise 2 Page 294

If the ratios of consecutive y-values are equal, then the data can be modeled by an exponential function. If the difference of consecutive y-values is constant, then the data can be modeled by a linear function.

Model: y=4x
Explanation: See solution.
Value of y When x=10: 40

Practice makes perfect

We want to write an appropriate model for the given data. Then we will use that model to find y when x=10. Let's do those things one at a time.

Writing the Model

If the ratios of consecutive y-values are equal, then the data can be modeled by an exponential function. If the difference of consecutive y-values is constant, then the data can be modeled by a linear function. Consider the given table.

x	0	1	2	3	4
y	0	4	8	12	16

Let's calculate the ratios of the consecutive y-values. 4/0&= undefined, 8/4= 2, [0.8em] 12/8&=1.5 , 16/12=1.333... We can see that the ratios are not equal to each other, so the data cannot be modeled by an exponential function. Let's determine the differences between the consecutive y-values. 4-0&= 4, 8-4= 4, 12-8&= 4, 16-12= 4 The difference of consecutive y-values is constant, so the data can be modeled by an linear function. y=mx+b To find the values of m and b, we will use two of the ordered pairs given in the table. For simplicity, we will use (0,0) and (1,4). Let's start by substituting 0 for x and for y.

y=mx+b

x= 0, y= 0

0=m( 0)+b

Zero Property of Multiplication

0=b

Rearrange equation

b=0

Now that we know that b= , we can partially write the equation. y=mx+ ⇔ y=mx To find the value of m, we will substitute 1 for x and 4 for y in the above equation.

y=mx

x= 1, y= 4

4=m( 1)

Identity Property of Multiplication

4=m

Rearrange equation

m=4

Now that we know that m=4, we can write the full equation that models the data in the given table. y=4x

Finding y When x=10

Finally, we will find the value of y when x=10. To do so, we will substitute 10 for x in the obtained formula.

y=4x

x= 10

y=4( 10)

Multiply

y=40

Subchapter links

Monitoring Progress p.294