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1. After Thanksgiving with her extended family, Surrena has a splitting headache. To take the edge off the pain, she takes an 800-mg tablet of ibuprofen. Ibuprofen in the human body has a half-life of approximately 1.8 hours. (a) Write a formula for a function that tells how much ibuprofen is in Surrena's system t hours after she takes the pill, assuming that she does not take any other pills. (b) If Surrena takes a pill every eight hours after taking the first one, what is the minimum amount of ibuprofen in her body at any given time? (c) After Surrena takes the first pill, how long will it take for the amount of ibuprofen in her body to drop below 300 milligrams?

1. After Thanksgiving with her extended family, Surrena has a splitting headache. To take the edge off the pain, she takes an 800-mg tablet of ibuprofen. Ibuprofen in the human body has a half-life of approximately 1.8 hours. (a) Write a formula for a function that tells how much ibuprofen is in Surrena's system t hours after she takes the pill, assuming that she does not take any other pills. (b) If Surrena takes a pill every eight hours after taking the first one, what is the minimum amount of ibuprofen in her body at any given time? (c) After Surrena takes the first pill, how long will it take for the amount of ibuprofen in her body to drop below 300 milligrams?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. After Thanksgiving with her extended family, Surrena has a splitting headache. To take the edge off the pain, she takes an 800-mg tablet of ibuprofen. Ibuprofen in the human body has a half-life of approximately 1.8 hours. (a) Write a formula for a function that tells how much ibuprofen is in Surrena’s system t hours after she takes the pill, assuming that she does not take any other pills. (b) If Surrena takes a pill every eight hours after taking the first one, what is the minimum amount of ibuprofen in her body at any given time? (c) After Surrena takes the first pill, how long will it take for the amount of ibuprofen in her body to drop below 300 milligrams?
**MAT 1093 – Precalculus** **Practice Mathematics Writing Assignment – Module 15** In this activity, we practice writing exponential functions to model quantities that grow or decay at constant relative (percent) rates. Keep in mind that any exponential function can be written in the form \( y = ab^t \), where \( a \) and \( b \) are nonzero constants (NOTE: either of these may be positive or negative). We can usually find appropriate values of \( a \) and \( b \) for a given situation by using known values of the function for specific values of \( t \). Here are some other forms of exponential functions that can be useful. Note that any exponential functions can be written in any of these forms; which form to use is mostly a matter of convenience and algebraic reasoning. - Known initial value and known growth factor (per unit time): - Known initial value and known growth factor (per units time): - Known initial value and known doubling time or half-life: - Doubling: \( y = a(2)^{t/h} \) - Halving: \( y = a(0.5)^{t/h} \) - Known initial value and known continuous growth or decay rate: \( y = ae^{kt} \) 1. **After Thanksgiving with her extended family, Surrena has a splitting headache. To take the edge off the pain, she takes an 800-mg tablet of ibuprofen. Ibuprofen in the human body has a half-life of approximately 1.8 hours.** (a) Write a formula for a function that tells how much ibuprofen is in Surrena’s system \( t \) hours after she takes the pill, assuming that she does not take any other pills. (b) If Surrena takes a pill every eight hours after taking the first one, what is the minimum amount of ibuprofen in her body at any given time? (c) After Surrena takes the first pill, how long will it take for the amount of ibuprofen in her body to drop below 300 milligrams?
Transcribed Image Text:**MAT 1093 – Precalculus** **Practice Mathematics Writing Assignment – Module 15** In this activity, we practice writing exponential functions to model quantities that grow or decay at constant relative (percent) rates. Keep in mind that any exponential function can be written in the form \( y = ab^t \), where \( a \) and \( b \) are nonzero constants (NOTE: either of these may be positive or negative). We can usually find appropriate values of \( a \) and \( b \) for a given situation by using known values of the function for specific values of \( t \). Here are some other forms of exponential functions that can be useful. Note that any exponential functions can be written in any of these forms; which form to use is mostly a matter of convenience and algebraic reasoning. - Known initial value and known growth factor (per unit time): - Known initial value and known growth factor (per units time): - Known initial value and known doubling time or half-life: - Doubling: \( y = a(2)^{t/h} \) - Halving: \( y = a(0.5)^{t/h} \) - Known initial value and known continuous growth or decay rate: \( y = ae^{kt} \) 1. **After Thanksgiving with her extended family, Surrena has a splitting headache. To take the edge off the pain, she takes an 800-mg tablet of ibuprofen. Ibuprofen in the human body has a half-life of approximately 1.8 hours.** (a) Write a formula for a function that tells how much ibuprofen is in Surrena’s system \( t \) hours after she takes the pill, assuming that she does not take any other pills. (b) If Surrena takes a pill every eight hours after taking the first one, what is the minimum amount of ibuprofen in her body at any given time? (c) After Surrena takes the first pill, how long will it take for the amount of ibuprofen in her body to drop below 300 milligrams?
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