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Common Core: High School - Functions : Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

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Example Questions

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=46(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Possible Answers:

$\\P_{days}(t)=46(16216)^t$

$\\P_{days}(t)=46(1677216)^t$

$\\P_{days}(t)=46(2)^{24t}$

$\\P_{days}(t)=46(16777216)^{2t}$

$\\P_{days}(t)=46(16777216)^t$

Correct answer:

$\\P_{days}(t)=46(16777216)^t$

Explanation:

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.A).

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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=46(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\\P_{hours}(24x)=46(2^{24})^x \\P_{hours}(24x)=46(16777216)^x \\P_{days}(t)=46(16777216)^t$

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Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=34(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Possible Answers:

$P_{days}(t)=34(16777216)^t$

$P_{days}(t)=3416780216^t$

$P_{days}(t)=34(16877216)^t$

$P_{days}(t)=34116780216^t$

$P_{days}(t)=34(16780216)^t$

Correct answer:

$P_{days}(t)=34(16777216)^t$

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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=34(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\\P_{hours}(24x)=34(2^{24})^x \\P_{hours}(24x)=34(16777216)^x \\P_{days}(t)=34(16777216)^t$

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Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=34(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Possible Answers:

$P_{minutes}(t)=34(10120)^t$

$P_{minutes}(t)=34(101.2)^t$

$P_{minutes}(t)=34(10.12)^t$

$P_{minutes}(t)=34(1012)^t$

$P_{minutes}(t)=34(1.012)^t$

Correct answer:

$P_{minutes}(t)=34(1.012)^t$

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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=34(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\\P_{minutes}\left(\frac{x}{60} \right )=34(2^{\frac{1}{60}})^x \\\\P_{minutes}\left(\frac{x}{60} \right )=34(1.012)^x \\P_{minutes}(t)=34(1.012)^t$

Report an Error

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=49(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Possible Answers:

$P_{minutes}(t)=46(1.012)^t$

$P_{minutes}(t)=49(10.12)^t$

$P_{minutes}(t)=46(10.12)^t$

$P_{minutes}(t)=49(1.012)^t$

$P_{minutes}(t)=49(101.2)^t$

Correct answer:

$P_{minutes}(t)=49(1.012)^t$

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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=49(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\\P_{minutes}\left(\frac{x}{60} \right )=49(2^{\frac{1}{60}})^x \\\\P_{minutes}\left(\frac{x}{60} \right )=49(1.012)^x \\P_{minutes}(t)=49(1.012)^t$

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Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=12(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Possible Answers:

$P_{days}(t)=12(167216)^t$

$P_{days}(t)=1216777216^t$

$P_{days}(t)=12(16777216)^t$

$P_{days}(t)=12(16216)^t$

$P_{days}(t)=12(1677216)^t$

Correct answer:

$P_{days}(t)=12(16777216)^t$

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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=12(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\\P_{hours}(24x)=12(2^{24})^x \\P_{hours}(24x)=12(16777216)^x \\P_{days}(t)=12(16777216)^t$

Report an Error

Example Question #3 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=9(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Possible Answers:

$P_{minutes}(t)=9(101.2)^t$

$P_{minutes}(t)=9(10.12)^t$

$P_{minutes}(t)=9(1.012)^t$

$P_{minutes}(t)=9.012^t$

$P_{minutes}(t)=9(1012)^t$

Correct answer:

$P_{minutes}(t)=9(1.012)^t$

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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=9(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\\P_{minutes}\left(\frac{x}{60} \right )=9(2^{\frac{1}{60}})^x \\\\P_{minutes}\left(\frac{x}{60} \right )=9(1.012)^x \\P_{minutes}(t)=9(1.012)^t$

Report an Error

Example Question #7 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=4(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Possible Answers:

$P_{days}(t)=4(16777216)^t$

$P_{days}(t)=4(177216)^t$

$P_{days}(t)=4(17777216)^t$

$P_{days}(t)=416777216^t$

$P_{days}(t)=4(16777)^t$

Correct answer:

$P_{days}(t)=4(16777216)^t$

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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=4(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\\P_{hours}(24x)=4(2^{24})^x \\P_{hours}(24x)=4(16777216)^x \\P_{days}(t)=4(16777216)^t$

Report an Error

Example Question #8 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=14(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Possible Answers:

$P_{minutes}(t)=14(1012)^t$

$P_{minutes}(t)=14.012^t$

$P_{minutes}(t)=14(101.2)^t$

$P_{minutes}(t)=14(10.12)^t$

$P_{minutes}(t)=14(1.012)^t$

Correct answer:

$P_{minutes}(t)=14(1.012)^t$

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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=14(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\\P_{minutes}\left(\frac{x}{60} \right )=14(2^{\frac{1}{60}})^x \\\\P_{minutes}\left(\frac{x}{60} \right )=14(1.012)^x \\P_{minutes}(t)=14(1.012)^t$

Report an Error

Example Question #9 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

$P_{hours}(x)=68(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Possible Answers:

$P_{minutes}(t)=68(1.012)^t$

$P_{minutes}(t)=68(10.12)^t$

$P_{minutes}(t)=68.012^t$

$P_{minutes}(t)=68(101.2)^t$

$P_{minutes}(t)=68.076^t$

Correct answer:

$P_{minutes}(t)=68(1.012)^t$

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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=68(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\\P_{minutes}\left(\frac{x}{60} \right )=68(2^{\frac{1}{60}})^x \\\\P_{minutes}\left(\frac{x}{60} \right )=68(1.012)^x \\P_{minutes}(t)=68(1.012)^t$

Report an Error

Example Question #7 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting 168 prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=168(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Possible Answers:

$P_{minutes}(t)=168.012^t$

$P_{minutes}(t)=168(2.02)^t$

$P_{minutes}(t)=160(2.012)^t$

$P_{minutes}(t)=168(2.012)^t$

$P_{minutes}(t)=168(1.012)^t$

Correct answer:

$P_{minutes}(t)=168(1.012)^t$

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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=168(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\\P_{minutes}\left(\frac{x}{60} \right )=168(2^{\frac{1}{60}})^x \\\\P_{minutes}\left(\frac{x}{60} \right )=168(1.012)^x \\P_{minutes}(t)=168(1.012)^t$

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Common Core: High School - Functions : Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #1 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #3 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #7 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #8 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #9 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

Example Question #7 : Constant Rate Of Change: Ccss.Math.Content.Hsf Le.A.1b

All Common Core: High School - Functions Resources

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