body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

Mathematical Practices

Continue to next subchapter

Exercise 1 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=2^x
Explanation: See solution.
Value of y When x=10: 1024

Practice makes perfect

We want to write an appropriate model for the given data. Then we will use the 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	1	2	4	8	16

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

y=ab^x

x= 0, y= 1

1=ab^0

▼

Solve for a

a^0=1

1=a(1)

Identity Property of Multiplication

1=a

Rearrange equation

a=1

Now that we know that a=1, we can partially write the equation. y=1b^x ⇔ y=b^x To find the value of b, we will substitute 1 for x and 2 for y in the above equation.

y=b^x

x= 1, y= 2

2=b^1

a^1=a

2=b

Rearrange equation

b=2

Now that we know that b=2, we can write the full equation that models the data in the given table. y=2^x

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=2^x

x= 10

y=2^(10)

Calculate power

y=1024

Subchapter links

Monitoring Progress p.294