Homework Help is Here – Start Your Trial Now!
Math
Calculus
When you drink coffee, you can describe the concentration of caffeine in your blood by the formula c(t) = Ax ekt c(t) is the concentration of caffeine t hours after consumption. k is a constant, which depends on your weight and we assume k = -0.5. A is the number of coffees you drink. Round all numbers to two decimals! a) When you drink a double shot of coffee. What is the function c(t) of your caffeine concentration? b) What is the concentration of caffeine two hours after the consumption of one cup? 9 How many coffees must you drink to have at least a dose of one coffee in the blood 4 hours later? d) How long does it take until your caffeine level half of the initial level? e) Derive c(t) and calculate the marginal decline of caffeine concentration 2 hours after you drank the two coffees. What does this number express? ) After learning that the half-life of caffeine concentration in the blood is 6 hours, we must adjust the value of k. What must be the correct value of k?

When you drink coffee, you can describe the concentration of caffeine in your blood by the formula c(t) = Ax ekt c(t) is the concentration of caffeine t hours after consumption. k is a constant, which depends on your weight and we assume k = -0.5. A is the number of coffees you drink. Round all numbers to two decimals! a) When you drink a double shot of coffee. What is the function c(t) of your caffeine concentration? b) What is the concentration of caffeine two hours after the consumption of one cup? 9 How many coffees must you drink to have at least a dose of one coffee in the blood 4 hours later? d) How long does it take until your caffeine level half of the initial level? e) Derive c(t) and calculate the marginal decline of caffeine concentration 2 hours after you drank the two coffees. What does this number express? ) After learning that the half-life of caffeine concentration in the blood is 6 hours, we must adjust the value of k. What must be the correct value of k?

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...
See similar textbooks
icon
Related questions
Question
100%

Hello,

I only need the solution for e and f, as you can see I already have the solutions from a to d.

Thanks.

 

Mahboob

Step 2 d) We have to find how long it takes for caffeine level to become half of initial level. We have calculated above that for one cup the initial caffeine level is 1. We have to find at what value of t, c(t) becomes 0.5. Thus, 0.5 = 1xe-0.5x1 = In(0. 50) → In(0. 50) = -0. 693147 In(e-0.5x) - 0.5 x t - 0.5 xt =t = 1.39 The required answer is 1.39 hours.
Transcribed Image Text:Step 2 d) We have to find how long it takes for caffeine level to become half of initial level. We have calculated above that for one cup the initial caffeine level is 1. We have to find at what value of t, c(t) becomes 0.5. Thus, 0.5 = 1xe-0.5x1 = In(0. 50) → In(0. 50) = -0. 693147 In(e-0.5x) - 0.5 x t - 0.5 xt =t = 1.39 The required answer is 1.39 hours.
When you drink coffee, you can describe the concentration of caffeine in your blood by the formula c(t) = Ax eht c(t) is the concentration of caffeine t hours after consumption. k is a constant, which depends on your weight and we assume k = -0,5. A is the number of coffees you drink. Round all numbers to two decimals! a) When you drink a double shot of coffee. What is the function c(t) of your caffeine concentration? b) What is the concentration of caffeine two hours after the consumption of one cup? ) How many coffees must you drink to have at least a dose of one coffee in the blood 4 hours later? d) How long does it take until your caffeine level half of the initial level? e) Derive c(t) and calculate the marginal decline of caffeine concentration 2 hours after you drank the two coffees. What does this number express? 1) After learning that the half-life of caffeine concentration in the blood is 6 hours, we must adjust the value of k. What must be the correct value of k? We are given the equation, which determines the concentration of caffeine in the blood, as c(1) = Ax e where c(t) is the concentration of caffeine t hours after consumption, k= 0.5, and A is the number of cups of coffees consumed. a) When we drink a double shot of coffee, A = 2. Then, the concentration of coffee can be given by the equation c(t) = 2xe-051 b) After 2 hours of consuming one cup of coffee, the concentration of the caffeine is c(t) = 1xe-05x2 = e- = 0.37 c) We have to find the number the coffees to be consumed to have at least one dose of coffee remaining after 4 hours. First we find the dose of one coffee. Here, A = 1, and t= 0 hours. Then, c (1) = Axe-0.5xI = 1 Now, we have to find the number of cups of coffee required so that the concentration of caffeine is same as ci(1) after 4 hours. Thus, 1 = Axe-05x4 >A = + = 2 > A = 7.4 So, the minimum number of cups is 7.4 cups.
Transcribed Image Text:When you drink coffee, you can describe the concentration of caffeine in your blood by the formula c(t) = Ax eht c(t) is the concentration of caffeine t hours after consumption. k is a constant, which depends on your weight and we assume k = -0,5. A is the number of coffees you drink. Round all numbers to two decimals! a) When you drink a double shot of coffee. What is the function c(t) of your caffeine concentration? b) What is the concentration of caffeine two hours after the consumption of one cup? ) How many coffees must you drink to have at least a dose of one coffee in the blood 4 hours later? d) How long does it take until your caffeine level half of the initial level? e) Derive c(t) and calculate the marginal decline of caffeine concentration 2 hours after you drank the two coffees. What does this number express? 1) After learning that the half-life of caffeine concentration in the blood is 6 hours, we must adjust the value of k. What must be the correct value of k? We are given the equation, which determines the concentration of caffeine in the blood, as c(1) = Ax e where c(t) is the concentration of caffeine t hours after consumption, k= 0.5, and A is the number of cups of coffees consumed. a) When we drink a double shot of coffee, A = 2. Then, the concentration of coffee can be given by the equation c(t) = 2xe-051 b) After 2 hours of consuming one cup of coffee, the concentration of the caffeine is c(t) = 1xe-05x2 = e- = 0.37 c) We have to find the number the coffees to be consumed to have at least one dose of coffee remaining after 4 hours. First we find the dose of one coffee. Here, A = 1, and t= 0 hours. Then, c (1) = Axe-0.5xI = 1 Now, we have to find the number of cups of coffee required so that the concentration of caffeine is same as ci(1) after 4 hours. Thus, 1 = Axe-05x4 >A = + = 2 > A = 7.4 So, the minimum number of cups is 7.4 cups.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS