Growth and Decay by Contant Percent Rate: CCSS.Math.Content.HSF-LE.A.1c - Common Core: High School - Functions

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Question

An anti-diabetic drug, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=500\textup{ mg} \h=\textup{half life}=6.2\textup{ hours} \t_f=4:34\textup{pm} \t_i=8:21\textup{ am} \A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=500\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{6.2}}$

$A=500\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.325}$

$A=500\textup{ mg}\cdot 0.399$

$A=199.57\textup{ mg}$

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Question

An anti-diabetic drug, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=200\textup{ mg} \h=\textup{half life}=4\textup{ hours} \t_f=1:00\textup{ pm} \t_i=8:00\textup{ am} \A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=200\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{4}}$

$A=200\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.25}$

$A=200\textup{ mg}\cdot 0.420$

$A=84\textup{ mg}$

Compare your answer with the correct one above

Question

An particular medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=50\textup{ mg} \h=\textup{half life}=3\textup{ hours} \t_f=2:00\textup{ pm} \t_i=11:00\textup{ am} \A=?$

Step 2: Calculate .

$2:00-11:00\rightarrow 3 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{3}{3}}$

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1}$

$A=50\textup{ mg}\cdot 0.50$

$A=25\textup{ mg}$

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Question

An particular medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=600\textup{ mg} \h=\textup{half life}=7\textup{ hours} \t_f=1:00\textup{ pm} \t_i=8:00\textup{ am} \A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=600\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{7}}$

$A=600\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.714}$

$A=600\textup{ mg}\cdot 0.61$

$A=366\textup{ mg}$

Compare your answer with the correct one above

Question

An particular medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=350\textup{ mg} \h=\textup{half life}=6\textup{ hours} \t_f=1:00\textup{ pm} \t_i=8:00\textup{ am} \A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=350\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{6}}$

$A=350\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.833}$

$A=350\textup{ mg}\cdot 0.561$

$A=196.35\textup{ mg}$

Compare your answer with the correct one above

Question

An anti-diabetic drug, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=800\textup{ mg} \h=\textup{half life}=6.2\textup{ hours} \t_f=4:34\textup{pm} \t_i=8:21\textup{ am} \A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{6.2}}$

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.325}$

$A=800\textup{ mg}\cdot 0.399$

$A=319.2\textup{ mg}$

Compare your answer with the correct one above

Question

An anti-diabetic drug, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=50\textup{ mg} \h=\textup{half life}=6.2\textup{ hours} \t_f=4:34\textup{pm} \t_i=8:21\textup{ am} \A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{6.2}}$

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.325}$

$A=50\textup{ mg}\cdot 0.399$

$A=19.95\textup{ mg}$

Compare your answer with the correct one above

Question

An medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=100\textup{ mg} \h=\textup{half life}=4.2\textup{ hours} \t_f=4:34\textup{pm} \t_i=8:21\textup{ am} \A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=100\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{4.2}}$

$A=100\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.9563}$

$A=100\textup{ mg}\cdot 0.2577$

$A=25.77\textup{ mg}$

Compare your answer with the correct one above

Question

An certain medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=150\textup{ mg} \h=\textup{half life}=3.4\textup{ hours} \t_f=4:34\textup{pm} \t_i=8:21\textup{ am} \A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=150\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{3.4}}$

$A=150\textup{ mg}\cdot \left(\frac{1}{2}\right)^{2.4166}$

$A=150\textup{ mg}\cdot 0.1873$

$A=28.09\textup{ mg}$

Compare your answer with the correct one above

Question

An particular medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=800\textup{ mg} \h=\textup{half life}=8\textup{ hours} \t_f=1:00\textup{ pm} \t_i=8:00\textup{ am} \A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{8}}$

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.625}$

$A=800\textup{ mg}\cdot 0.6484$

$A=518.72\textup{ mg}$

Compare your answer with the correct one above

Question

An particular medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=600\textup{ mg} \h=\textup{half life}=4\textup{ hours} \t_f=2:00\textup{ pm} \t_i=9:00\textup{ am} \A=?$

Step 2: Calculate .

$2:00-9:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=600\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{4}}$

$A=600\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.25}$

$A=600\textup{ mg}\cdot 0.4204$

$A=252.24\textup{ mg}$

Compare your answer with the correct one above

Question

An particular medicine, has a half-life of about hours. If a patient was administered of the drug at , how much is left at ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Answer

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, 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 the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\A_0=\textup{Intial Amount}=400\textup{ mg} \h=\textup{half life}=5.8\textup{ hours} \t_f=2:00\textup{ pm} \t_i=9:00\textup{ am} \A=?$

Step 2: Calculate .

$2:00-9:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=400\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{5.8}}$

$A=400\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.8621}$

$A=400\textup{ mg}\cdot 0.5502$

$A=220.08\textup{ mg}$

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