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

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Common Core: High School - Functions › Properties of Exponents: CCSS.Math.Content.HSF-IF.C.8b

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

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

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

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

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

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

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.67\times 100=67%$ .

Step 4: Answer question.

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

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

$\ \textup{Percent rate of change: } 66% \ \textup{Exponential Decay}$

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

$\ \textup{Percent rate of change: } 66% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 34% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 34% \ \textup{Exponential Growth}$

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.

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.66\times 100=66%$ .

Step 4: Answer question.

$\ \textup{Percent rate of change: } 66% \ \textup{Exponential Decay}$

A savings account has an interest rate of compounded annually. If Bob deposits into the account how much money will he have in his savings account after years?

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 and function values at specific input values.

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.

The question is asking for the Bob's account balance after 6 years.

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

I. represents an exponential growth function.

II. represents an exponential decay function.

Step 3: Identify what is known.

$\r=\textup{rate}=1.5% \a=\textup{Initial Deposit}=$55.00 \x=\textup{Time}=6$

Step 4: Substitute the known values into the growth function.

$\f(6)=a(1+r)^x \f(6)=$55.00(1+.015)^6 \f(6)=$55.00(1.0934) \f(6)=$60.14$

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

$\ \textup{Percent rate of change: } 20% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 20% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 10% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 80% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 80% \ \textup{Exponential Decay}$

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.20\times 100=20%$ .

Step 4: Answer question.

$\ \textup{Percent rate of change: } 20% \ \textup{Exponential Growth}$

Given the following function determine if it is exponentially growing or decaying and the function value when is .

$\ f(3)=0.448 \ \textup{Exponential Decay}$

$\ f(3)=0.448 \ \textup{Exponential Growth}$

$\ f(3)=1.448 \ \textup{Exponential Decay}$

$\ f(3)=1.448 \ \textup{Exponential Growth}$

$\ f(3)=0.648 \ \textup{Exponential Decay}$

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 function value at 3.

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

I. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential decay.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.28\times 100=28%$ .

Step 4: Answer question.

$\ \textup{Percent rate of change: } 28% \ \textup{Exponential Decay}$

Step 5: Find the function value at 3.

$\f(x)=1.2(0.72)^x \f(3)=1.2(0.72)^3 \f(3)=0.4479\f(3)=0.448$

Tina invests $$1\textup,250$ into an account where it accumulates at an interest rate of annually. After years how much money does Tina have?

Explanation

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.

The question is asking for the amount of money Tina has many after investing for ten years.

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

I. represents an exponential growth function.

II. represents an exponential decay function.

Step 3: Identify what is known.

$\r=\textup{rate}=3.7% \a=\textup{Initial Deposit}=$1250.00 \x=\textup{Time}=10$

Step 4: Substitute the known values into the growth function.

$\f(10)=a(1+r)^x \f(10)=$1250.00(1+.037)^{10} \f(10)=$1797.62$

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

$\ \textup{Percent rate of change: } 13% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 13% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 15% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 87% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 87% \ \textup{Exponential Growth}$

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.

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.13\times 100=13%$ .

Step 4: Answer question.

$\ \textup{Percent rate of change: } 13% \ \textup{Exponential Decay}$

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

$\ \textup{Percent rate of change: } 11% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 11% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 89% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 89% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 10% \ \textup{Exponential Decay}$

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.11\times 100=11%$ .

Step 4: Answer question.

$\ \textup{Percent rate of change: } 11% \ \textup{Exponential Decay}$

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

$\ \textup{Percent rate of change: } 14% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 14% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 104% \ \textup{Exponential Growth}$

$\ \textup{Percent rate of change: } 104% \ \textup{Exponential Decay}$

$\ \textup{Percent rate of change: } 24% \ \textup{Exponential Growth}$

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.

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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

$0.14\times 100=14%$ .

Step 4: Answer question.

$\ \textup{Percent rate of change: } 14% \ \textup{Exponential Growth}$

Find the percent rate of change for the following function.

Identify whether the function is exponential growth or exponential decay.

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

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

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

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

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

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. represents an exponential growth function.

II. 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,

use the above expressions to help solve.

Since

the functions can be defined as exponential decay.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

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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