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

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Example Question #1 : 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

Possible Answers:

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

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

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

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

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

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.

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

Report an Error

Example Question #2 : 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.

Possible Answers:

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

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

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

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

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

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.

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

Report an Error

Example Question #3 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Determine the percent rate of change for the following function.

y=10(0.5)^x

Does the function represent an exponential growth or decay?

Possible Answers:

$\\ \textup{Percent rate of change: } 25\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 50\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 5\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 5\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 50\% \\ \textup{Exponential Growth}$

Correct answer:

$\\ \textup{Percent rate of change: } 50\% \\ \textup{Exponential Decay}$

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=10(0.5)^x

use the above expressions to help solve.

Since

0.50=1-r; r=0.50

the functions can be defined as exponential decay.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.50=1-r; r=0.50

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

$0.50\times 100=50\%$ .

Step 4: Answer question.

$\\ \textup{Percent rate of change: } 50\% \\ \textup{Exponential Decay}$

Report an Error

Example Question #4 : 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(1.14)^x

Possible Answers:

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

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

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

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

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

Correct answer:

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

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. 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(1.14)^x

use the above expressions to help solve.

Since

1.14=1+r; r=0.14

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

1.14=1+r; r=0.14

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

$0.14\times 100=14\%$ .

Step 4: Answer question.

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

Report an Error

Example Question #5 : 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=5(0.87)^x

Possible Answers:

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

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

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

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

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

Correct answer:

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

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=5(0.87)^x

use the above expressions to help solve.

Since

0.87=1-r; r=0.13

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.87=1-r; r=0.13

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

$0.13\times 100=13\%$ .

Step 4: Answer question.

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

Report an Error

Example Question #6 : 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=(1.20)^x

Possible Answers:

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

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

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

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

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

Correct answer:

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

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. 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=(1.20)^x

use the above expressions to help solve.

Since

1.20=1+r; r=0.20

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

1.20=1+r; r=0.20

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

$0.20\times 100=20\%$ .

Step 4: Answer question.

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

Report an Error

Example Question #7 : 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=(0.34)^x

Possible Answers:

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

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

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

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

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

Correct answer:

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

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=(0.34)^x

use the above expressions to help solve.

Since

0.34=1-r; r=0.66

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.34=1-r; r=0.66

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

$0.66\times 100=66\%$ .

Step 4: Answer question.

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

Report an Error

Example Question #8 : 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=(0.89)^x

Possible Answers:

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

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

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

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

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

Correct answer:

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

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=(0.89)^x

use the above expressions to help solve.

Since

0.89=1-r; r=0.11

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.89=1-r; r=0.11

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

$0.11\times 100=11\%$ .

Step 4: Answer question.

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

Report an Error

Example Question #9 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

A savings account has an interest rate of $1.5\%$ compounded annually. If Bob deposits $\$55.00$ into the account how much money will he have in his savings account after years?

Possible Answers:

$\$60.14$

$\$59.10$

$\$65.14$

$\$62.27$

$\$66.70$

Correct answer:

$\$60.14$

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

II. a(1-r)^x 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.

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

Report an Error

Example Question #10 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Janet has a student loan of $\$3\textup,500$ . The company that is financing the loan has an annual interest rate of $2.67\%$ . If Janet waits two years to start paying off her loan, how much interest will have accumulated?

Possible Answers:

$\$189.14$

$\$198.40$

$\$190.40$

$\$189.40$

$\$2.40$

Correct answer:

$\$189.40$

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 interest that will be added to the loan after two years.

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: Identify what is known.

$\\r=\textup{rate}=2.67\% \\a=\textup{Initial Deposit}=\$3500.00 \\x=\textup{Time}=2$

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

$\\f(2)=a(1+r)^x \\f(6)=\$3500.00(1+.0267)^2 \\f(2)=\$3689.40$

Step 5: Calculate the amount of interest.

To calculate the amount of interest, subtract the initial amount from the final amount found in step 4.

$\\ \textup{Interest}=\textup{Final Amount}-\textup{Initial Amount} \\\textup{Interest}=\$3689.40-\$3500.00 \\\textup{Interest}=\$189.40$

Report an Error

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

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

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Example Question #1 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

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Example Question #8 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #9 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

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All Common Core: High School - Functions Resources

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