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Math Calculus Calculus For The Life Sciences

Drug Concentration When a pharmaceutical drug is injected into the bloodstream, its concentration at time t can be approximated by C t = C o e - k t , where C o is the concentration at t = 0 . Suppose the drug is ineffective below a concentration C 1 and harmful above a concentration C 2 . Then it can be shown that the drug should be given at intervals of time T , where T = 1 k ln ⁡ C 2 C 1 Source: Applications of Calculus to Medicine. A certain drug is harmful at a concentration five times the concentration below which it is ineffective. At noon an injection of the drug results in a concentration of 2 mg per liter of blood. Three hours later the concentration is down to 1 mg per liter. How often should the drug be given?

Drug Concentration When a pharmaceutical drug is injected into the bloodstream, its concentration at time t can be approximated by C t = C o e - k t , where C o is the concentration at t = 0 . Suppose the drug is ineffective below a concentration C 1 and harmful above a concentration C 2 . Then it can be shown that the drug should be given at intervals of time T , where T = 1 k ln ⁡ C 2 C 1 Source: Applications of Calculus to Medicine. A certain drug is harmful at a concentration five times the concentration below which it is ineffective. At noon an injection of the drug results in a concentration of 2 mg per liter of blood. Three hours later the concentration is down to 1 mg per liter. How often should the drug be given?

Solution Summary: The author explains that the time when a drug is injected again due to it being harmful is approximated by C(t)=C_oe-kt

Calculus For The Life Sciences

Calculus For The Life Sciences

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 2.2, Problem 87E

Drug Concentration When a pharmaceutical drug is injected into the bloodstream, its concentration at time t can be approximated by C t = C o e - k t , where C o is the concentration at t = 0 . Suppose the drug is ineffective below a concentration C 1 and harmful above a concentration C 2 . Then it can be shown that the drug should be given at intervals of time T , where

T = 1 k ln ⁡ C 2 C 1

Source: Applications of Calculus to Medicine.

A certain drug is harmful at a concentration five times the concentration below which it is ineffective. At noon an injection of the drug results in a concentration of 2 mg per liter of blood. Three hours later the concentration is down to 1 mg per liter. How often should the drug be given?

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Chapter 2.2, Problem 86E

Chapter 2.2, Problem 88E

Chapter 2 Solutions

Calculus For The Life Sciences

Ch. 2.1 - YOUR TURN Solve 25x2=125x+3 Ch. 2.1 - Prob. 2YT Ch. 2.1 - YOUR TURN Find the amount after 4 years if 800 is...Ch. 2.1 - A ream of 20-lb paper contains 500 sheets and is...Ch. 2.1 - A ream of 20-lb paper contains 500 sheets and is...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...

Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - In Exercises3-11, there were more formulas for...Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Solve each equation. ex=1e5 Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Solve each equation. 16x+3=642x-5 Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - A friend claims that as x becomes large, the...Ch. 2.1 - Prob. 37E Ch. 2.1 - Growth of Bacteria Salmonella bacteria, found on...Ch. 2.1 - Prob. 39E Ch. 2.1 - Physician Demand The demand for physicians is...Ch. 2.1 - Prob. 41E Ch. 2.1 - Bacteria in Sausage The number of Enterococcus...Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Cortisone Concentration A mathematical model for...Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 50E Ch. 2.1 - Interest Find the interest earned on 10,000...Ch. 2.1 - Prob. 52E Ch. 2.1 - Interest Ron Hampton needs to choose between two...Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Interest Leigh Jacks plans to invest 500 into a...Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Interest On January 1, 2000, Jack deposited 1000...Ch. 2.2 - YOUR TURN Write the equation in logarithmic...Ch. 2.2 - Prob. 2YT Ch. 2.2 - YOUR TURN Write the expression logax2/y3 as a sum,...Ch. 2.2 - Prob. 4YT Ch. 2.2 - YOUR TURN Solve for x: log2x+log2x+2=3 Ch. 2.2 - YOUR TURN 6 Solve for x: 2x+1=3x Ch. 2.2 - Prob. 7YT Ch. 2.2 - Write each exponential equation in logarithmic...Ch. 2.2 - Prob. 2E Ch. 2.2 - Write each exponential equation in logarithmic...Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Evaluate each logarithm without using a...Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - Prob. 20E Ch. 2.2 - Prob. 21E Ch. 2.2 - Prob. 22E Ch. 2.2 - Prob. 23E Ch. 2.2 - Prob. 24E Ch. 2.2 - Prob. 25E Ch. 2.2 - Prob. 26E Ch. 2.2 - Prob. 27E Ch. 2.2 - Prob. 28E Ch. 2.2 - Prob. 29E Ch. 2.2 - Prob. 30E Ch. 2.2 - Prob. 31E Ch. 2.2 - Prob. 32E Ch. 2.2 - Prob. 33E Ch. 2.2 - Suppose logb2=a and logb3=c. Use the properties of...Ch. 2.2 - Prob. 35E Ch. 2.2 - Prob. 36E Ch. 2.2 - Prob. 37E Ch. 2.2 - Prob. 38E Ch. 2.2 - Prob. 39E Ch. 2.2 - Prob. 40E Ch. 2.2 - Prob. 41E Ch. 2.2 - Prob. 42E Ch. 2.2 - Prob. 43E Ch. 2.2 - Prob. 44E Ch. 2.2 - Prob. 45E Ch. 2.2 - Prob. 46E Ch. 2.2 - Prob. 47E Ch. 2.2 - Prob. 48E Ch. 2.2 - Prob. 49E Ch. 2.2 - Prob. 50E Ch. 2.2 - Prob. 51E Ch. 2.2 - Prob. 52E Ch. 2.2 - Prob. 53E Ch. 2.2 - Prob. 54E Ch. 2.2 - Prob. 55E Ch. 2.2 - Prob. 56E Ch. 2.2 - Prob. 57E Ch. 2.2 - Prob. 58E Ch. 2.2 - Prob. 59E Ch. 2.2 - Prob. 60E Ch. 2.2 - Prob. 61E Ch. 2.2 - Prob. 62E Ch. 2.2 - Solve each question in Exercises 41-64. Round...Ch. 2.2 - Solve each question in Exercises 41-64. Round...Ch. 2.2 - Write each expression using base e rather than...Ch. 2.2 - Prob. 66E Ch. 2.2 - Prob. 67E Ch. 2.2 - Approximate each expression in the form ax without...Ch. 2.2 - Prob. 69E Ch. 2.2 - Prob. 70E Ch. 2.2 - Prob. 71E Ch. 2.2 - Prob. 72E Ch. 2.2 - Prob. 73E Ch. 2.2 - Prob. 74E Ch. 2.2 - Prob. 75E Ch. 2.2 - Prob. 76E Ch. 2.2 - Minority Population The U.S. Census Bureau has...Ch. 2.2 - Bald Eagle Population The U.S. Fish & Wildlife...Ch. 2.2 - Population Growth Two species of squirrels inhabit...Ch. 2.2 - Population Growth In July 1994, the population of...Ch. 2.2 - Prob. 81E Ch. 2.2 - Prob. 82E Ch. 2.2 - Find the value of the index of diversity for...Ch. 2.2 - Prob. 84E Ch. 2.2 - Prob. 85E Ch. 2.2 - Prob. 86E Ch. 2.2 - Drug Concentration When a pharmaceutical drug is...Ch. 2.2 - Tumor Growth An article on growth rates of cancer...Ch. 2.2 - Prob. 89E Ch. 2.2 - Prob. 90E Ch. 2.2 - Torontos Jewish Population The table gives the...Ch. 2.2 - OTHER APPLICATIONS Music Theory A music theorist...Ch. 2.2 - OTHER APPLICATIONS Evolution of languages The...Ch. 2.2 - Prob. 94E Ch. 2.2 - Prob. 95E Ch. 2.2 - Earthquake Intensity The magnitude of an...Ch. 2.2 - Acidity of a solution A common measure for the...Ch. 2.3 - YOUR TURN Find the growth function if 5 g grows...Ch. 2.3 - Prob. 2YT Ch. 2.3 - In the exponential growth or decay function...Ch. 2.3 - Prob. 2E Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 4E Ch. 2.3 - Prob. 5E Ch. 2.3 - Prob. 6E Ch. 2.3 - Giardia When a person swallows giardia cysts,...Ch. 2.3 - Growth of Bacteria A culture contains 25,000...Ch. 2.3 - Decrease in Bacteria When an antibiotic is...Ch. 2.3 - Growth of Bacteria The growth of bacteria in food...Ch. 2.3 - Prob. 11E Ch. 2.3 - Chromosomal Abnormality The graph below shows how...Ch. 2.3 - Botany A group of Tasmanian botanists have claimed...Ch. 2.3 - Decay of Radioactivity A large cloud of...Ch. 2.3 - Prob. 15E Ch. 2.3 - Prob. 16E Ch. 2.3 - Carbon Dating Refer to Example 2. A sample from a...Ch. 2.3 - Half Life Find the half-life of each radioactive...Ch. 2.3 - Half Life Find the half life of each radioactive...Ch. 2.3 - Half-Life The half-life of plutonium-241 is...Ch. 2.3 - Half-Life The half-life of radium-226 is...Ch. 2.3 - Radioactive Decay 500 g of iodine-131 is decaying...Ch. 2.3 - Radioactive Decay 25 g of polonium-210 is decaying...Ch. 2.3 - Nuclear Energy Nuclear energy derived from...Ch. 2.3 - Chemical Dissolution The amount of chemical that...Ch. 2.3 - Newtons Law of Cooling Newtons law of cooling says...Ch. 2.3 - Newtons Law of Cooling Newtons law of cooling says...Ch. 2.3 - Newtons Law of Cooling Newtons law of cooling says...Ch. 2.4 - YOUR TURN a Convert 210 to radians. b Convert 3/4...Ch. 2.4 - Prob. 2YT Ch. 2.4 - Prob. 3YT Ch. 2.4 - Prob. 4YT Ch. 2.4 - Prob. 5YT Ch. 2.4 - Prob. 1E Ch. 2.4 - Prob. 2E Ch. 2.4 - Convert the following degree measures to radians....Ch. 2.4 - Prob. 4E Ch. 2.4 - Prob. 5E Ch. 2.4 - Prob. 6E Ch. 2.4 - Prob. 7E Ch. 2.4 - Prob. 8E Ch. 2.4 - Prob. 9E Ch. 2.4 - Prob. 10E Ch. 2.4 - Prob. 11E Ch. 2.4 - Prob. 12E Ch. 2.4 - Prob. 13E Ch. 2.4 - Prob. 14E Ch. 2.4 - Convert the following radian measures to degrees....Ch. 2.4 - Prob. 16E Ch. 2.4 - Prob. 17E Ch. 2.4 - Prob. 18E Ch. 2.4 - Prob. 19E Ch. 2.4 - Prob. 20E Ch. 2.4 - Prob. 21E Ch. 2.4 - Prob. 22E Ch. 2.4 - Prob. 23E Ch. 2.4 - Prob. 24E Ch. 2.4 - For Exercises 2532, complete the following table....Ch. 2.4 - Prob. 26E Ch. 2.4 - Prob. 27E Ch. 2.4 - Prob. 28E Ch. 2.4 - Prob. 29E Ch. 2.4 - For Exercises 2532, complete the following table....Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Prob. 35E Ch. 2.4 - Prob. 36E Ch. 2.4 - Prob. 37E Ch. 2.4 - Prob. 38E Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Prob. 40E Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Prob. 53E Ch. 2.4 - Prob. 54E Ch. 2.4 - Prob. 55E Ch. 2.4 - Prob. 56E Ch. 2.4 - Prob. 57E Ch. 2.4 - Prob. 58E Ch. 2.4 - Prob. 59E Ch. 2.4 - Use a calculator to find the following function...Ch. 2.4 - Prob. 61E Ch. 2.4 - Prob. 62E Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Prob. 75E Ch. 2.4 - Prob. 76E Ch. 2.4 - Prob. 77E Ch. 2.4 - Transylvania Hypothesis The Transylvania...Ch. 2.4 - Prob. 79E Ch. 2.4 - Prob. 80E Ch. 2.4 - Prob. 81E Ch. 2.4 - Prob. 82E Ch. 2.4 - Prob. 83E Ch. 2.4 - Prob. 84E Ch. 2.4 - Prob. 85E Ch. 2.4 - Prob. 86E Ch. 2.4 - Sound Suppose the A key above Middle C is played...Ch. 2.4 - Temperature The maximum afternoon temperature in...Ch. 2.4 - Temperature A mathematical model for the...Ch. 2.4 - Prob. 90E Ch. 2.4 - Prob. 91E Ch. 2.4 - Prob. 92E Ch. 2.CR - Prob. 1CR Ch. 2.CR - Prob. 2CR Ch. 2.CR - Prob. 3CR Ch. 2.CR - Prob. 4CR Ch. 2.CR - Determine whether each of the following statement...Ch. 2.CR - Prob. 6CR Ch. 2.CR - Prob. 7CR Ch. 2.CR - Prob. 8CR Ch. 2.CR - Prob. 9CR Ch. 2.CR - Prob. 10CR Ch. 2.CR - Prob. 11CR Ch. 2.CR - Prob. 12CR Ch. 2.CR - Prob. 13CR Ch. 2.CR - Prob. 14CR Ch. 2.CR - Prob. 15CR Ch. 2.CR - Prob. 16CR Ch. 2.CR - Prob. 17CR Ch. 2.CR - Prob. 18CR Ch. 2.CR - Prob. 19CR Ch. 2.CR - Prob. 20CR Ch. 2.CR - Prob. 21CR Ch. 2.CR - Prob. 22CR Ch. 2.CR - Prob. 23CR Ch. 2.CR - Prob. 24CR Ch. 2.CR - Prob. 25CR Ch. 2.CR - Prob. 26CR Ch. 2.CR - Prob. 27CR Ch. 2.CR - Prob. 28CR Ch. 2.CR - Prob. 29CR Ch. 2.CR - Prob. 30CR Ch. 2.CR - Prob. 31CR Ch. 2.CR - Prob. 32CR Ch. 2.CR - Prob. 33CR Ch. 2.CR - Prob. 34CR Ch. 2.CR - Prob. 35CR Ch. 2.CR - Prob. 36CR Ch. 2.CR - Prob. 37CR Ch. 2.CR - Prob. 38CR Ch. 2.CR - Prob. 39CR Ch. 2.CR - Prob. 40CR Ch. 2.CR - Prob. 41CR Ch. 2.CR - Prob. 42CR Ch. 2.CR - Prob. 43CR Ch. 2.CR - Prob. 44CR Ch. 2.CR - Prob. 45CR Ch. 2.CR - Prob. 46CR Ch. 2.CR - Prob. 47CR Ch. 2.CR - Prob. 48CR Ch. 2.CR - Prob. 49CR Ch. 2.CR - Prob. 50CR Ch. 2.CR - Prob. 51CR Ch. 2.CR - Prob. 52CR Ch. 2.CR - Prob. 53CR Ch. 2.CR - Prob. 54CR Ch. 2.CR - Prob. 55CR Ch. 2.CR - Prob. 56CR Ch. 2.CR - Prob. 57CR Ch. 2.CR - Prob. 58CR Ch. 2.CR - Prob. 59CR Ch. 2.CR - Prob. 60CR Ch. 2.CR - Prob. 61CR Ch. 2.CR - Prob. 62CR Ch. 2.CR - Prob. 63CR Ch. 2.CR - Prob. 64CR Ch. 2.CR - Prob. 65CR Ch. 2.CR - Prob. 66CR Ch. 2.CR - Prob. 67CR Ch. 2.CR - Prob. 68CR Ch. 2.CR - Prob. 69CR Ch. 2.CR - Prob. 70CR Ch. 2.CR - Prob. 71CR Ch. 2.CR - Prob. 72CR Ch. 2.CR - Prob. 73CR Ch. 2.CR - Prob. 74CR Ch. 2.CR - Prob. 75CR Ch. 2.CR - Prob. 76CR Ch. 2.CR - Prob. 77CR Ch. 2.CR - Prob. 78CR Ch. 2.CR - Prob. 79CR Ch. 2.CR - Prob. 80CR Ch. 2.CR - Prob. 81CR Ch. 2.CR - Prob. 82CR Ch. 2.CR - Prob. 83CR Ch. 2.CR - Prob. 84CR Ch. 2.CR - Prob. 85CR Ch. 2.CR - Prob. 86CR Ch. 2.CR - Prob. 87CR Ch. 2.CR - Prob. 88CR Ch. 2.CR - Prob. 89CR Ch. 2.CR - Prob. 90CR Ch. 2.CR - Find each function value without using a...Ch. 2.CR - Prob. 92CR Ch. 2.CR - Prob. 93CR Ch. 2.CR - Prob. 94CR Ch. 2.CR - Prob. 95CR Ch. 2.CR - Prob. 96CR Ch. 2.CR - Prob. 97CR Ch. 2.CR - Prob. 98CR Ch. 2.CR - Prob. 99CR Ch. 2.CR - Prob. 100CR Ch. 2.CR - Prob. 101CR Ch. 2.CR - Prob. 102CR Ch. 2.CR - Prob. 103CR Ch. 2.CR - Prob. 104CR Ch. 2.CR - Prob. 105CR Ch. 2.CR - Prob. 106CR Ch. 2.CR - Glucose Concentration When glucose is infused into...Ch. 2.CR - Prob. 108CR Ch. 2.CR - Cancer growth Cancer cells often have a diameter...Ch. 2.CR - Prob. 110CR Ch. 2.CR - Respiratory Rate Researchers have found that the...Ch. 2.CR - Prob. 112CR Ch. 2.CR - Prob. 113CR Ch. 2.CR - Prob. 114CR Ch. 2.CR - Prob. 115CR Ch. 2.CR - Prob. 116CR Ch. 2.CR - Prob. 117CR Ch. 2.CR - Prob. 118CR Ch. 2.CR - Prob. 119CR Ch. 2.CR - Prob. 120CR Ch. 2.CR - Prob. 121CR Ch. 2.CR - Prob. 122CR Ch. 2.CR - Prob. 123CR Ch. 2.CR - Prob. 124CR Ch. 2.CR - Prob. 125CR Ch. 2.CR - Prob. 126CR Ch. 2.CR - Temperature The table lists the average monthly...Ch. 2.EA - Determine whether each of the following statement...Ch. 2.EA - Prob. 2EA

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The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?

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