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All Common Core: High School - Functions Resources

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Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Determine the percent rate of change and whether the function represents exponential growth or decay.

y=2(1.67)^x

$\\ \textup{Percent rate of change: } 76\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 1.34\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 67\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 67\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 76\% \\ \textup{Exponential Decay}$

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Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Determine the percent rate of change and whether the function represents exponential growth or decay.

y=2(1.67)^x

Your answer:

$\\ \textup{Percent rate of change: } 76\% \\ \textup{Exponential Growth}$

Your answer:

$\\ \textup{Percent rate of change: } 1.34\% \\ \textup{Exponential Growth}$

Your answer:

$\\ \textup{Percent rate of change: } 67\% \\ \textup{Exponential Decay}$

Your answer:

$\\ \textup{Percent rate of change: } 76\% \\ \textup{Exponential Decay}$

Correct answer:

$\\ \textup{Percent rate of change: } 67\% \\ \textup{Exponential Growth}$

Explanation:

This question is testing one's ability to use properties of exponents to solve and interpret functions as well as identify key concepts of exponential growth and decay such as percent rate of change.

For the purpose of Common Core Standards, properties of exponents to interpret functions falls within the Cluster C of analyze functions using different representations concept (CCSS.Math.content.HSF-IF.C.8).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Calculate the percent rate of change.

Recall that in the previous expressions represent the rate. Therefore, to calculate the percent rate of change simply multiply by 100.

Step 4: Answer question.

Following the above steps to solve this particular question, results in the following.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2:

Use algebraic techniques to aid in solving the problem.

Given the function,

y=2(1.67)^x

use the above expressions to help solve.

Since

1.67=1+r; r=0.67

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

1.67=1+r; r=0.67

therefore to solve for percent rate of change multiply by 100.

$0.67\times 100=67\%$ .

Step 4: Answer question.

$\\ \textup{Percent rate of change: } 67\% \\ \textup{Exponential Growth}$

Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Find the percent rate of change for the following function.

y=0.83^x

Identify whether the function is exponential growth or exponential decay.

$\\ \textup{Percent rate of change: }19\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: }17\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: }-19\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: }19\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: }17\% \\ \textup{Exponential Decay}$

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Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Find the percent rate of change for the following function.

y=0.83^x

Identify whether the function is exponential growth or exponential decay.

Your answer:

$\\ \textup{Percent rate of change: }19\% \\ \textup{Exponential Decay}$

Your answer:

$\\ \textup{Percent rate of change: }17\% \\ \textup{Exponential Growth}$

Your answer:

$\\ \textup{Percent rate of change: }-19\% \\ \textup{Exponential Decay}$

Your answer:

$\\ \textup{Percent rate of change: }19\% \\ \textup{Exponential Growth}$

Correct answer:

$\\ \textup{Percent rate of change: }17\% \\ \textup{Exponential Decay}$

Explanation:

This question is testing one's ability to use properties of exponents to solve and interpret functions as well as identify key concepts of exponential growth and decay such as percent rate of change.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Calculate the percent rate of change.

Recall that in the previous expressions represent the rate. Therefore, to calculate the percent rate of change simply multiply by 100.

Step 4: Answer question.

Following the above steps to solve this particular question, results in the following.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2:

Use algebraic techniques to aid in solving the problem.

Given the function,

y=0.83^x

use the above expressions to help solve.

Since

0.83=1-r; r=0.17

the functions can be defined as exponential decay.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.83=1-r; r=0.17

therefore to solve for percent rate of change multiply by 100.

$0.17\times 100=17\%$ .

Step 4: Answer question.

$\\ \textup{Percent rate of change: } 17\% \\ \textup{Exponential Decay}$

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All Common Core: High School - Functions Resources

Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

Flashcards: Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

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