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Flashcards: 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 $\displaystyle 46$ prions, and each prion caused the misfolding of a new protein every $\displaystyle x$ number of hours, is illustrated by the following function.

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

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

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

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

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

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

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

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

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Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

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

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

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

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

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

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

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

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

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Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

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

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

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

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

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 $\displaystyle x$ is in terms of days as opposed to the given function which has $\displaystyle x$ in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

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

So if

$x=\textup{hour}$ $\displaystyle x=\textup{hour}$

then

$1\textup{ day}=24x$ $\displaystyle 1\textup{ day}=24x$

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

Given the original function:

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

Let $\displaystyle t$ represent time in days

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

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

Flashcards: 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 $\displaystyle 34$ prions, and each prion caused the misfolding of a new protein every $\displaystyle x$ number of hours, is illustrated by the following function.

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

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

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

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

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

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

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

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

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Flashcards: 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 $\displaystyle 34$ prions, and each prion caused the misfolding of a new protein every $\displaystyle x$ number of hours, is illustrated by the following function.

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

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

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

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

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 $\displaystyle x$ is in terms of days as opposed to the given function which has $\displaystyle x$ in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

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

So if

$x=\textup{hour}$ $\displaystyle x=\textup{hour}$

then

$1\textup{ day}=24x$ $\displaystyle 1\textup{ day}=24x$

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

Given the original function:

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

Let $\displaystyle t$ represent time in days

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

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

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Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

All Common Core: High School - Functions Resources

Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

Flashcards: Constant Rate of Change: CCSS.Math.Content.HSF-LE.A.1b

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