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Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

7. Modeling with Exponential and Logarithmic Functions

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Exercise 23 Page 347

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.

Exponential relationship of data: No.
Example model: $y = - 0.8 x + 66$
Explanation: See solution.

Practice makes perfect

We want to determine whether the data show an exponential relationship. Then we will write a function that models the data. Let's do those things one at a time.

Determining the Type of 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.

$x$	$0$	$10$	$20$	$30$	$40$	$50$	$60$
$y$	$66$	$58$	$48$	$42$	$31$	$26$	$21$

Let's calculate the ratios of the consecutive

y -

values.

Subchapter links

Communicate Your Answer p.341

Monitoring Progress p.342-345