After a large number of drinks a person has a blood-alcohol level of 200 mg/dl (milligrams per deciliter). Suppose the level of the alcohol in the blood is an exponential function f(x) = Ab^x mg/dl, where x is the number of hours elapsed. We know that after 3 hours 112.5 mg/dl remains in his blood. Find A and b and estimate the person’s blood alcohol after 4 hours. By what percentage is the blood alcohol level decreasing per hour?

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: ount of asprin decays exponentiallyf(t) = Ae-ktat t = 0 ,   300 = Ae0⇒ A = 300

Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

Q: A culture of bacteria originally numbers 500. After 2 hours there are 1500 bacteria in the culture.…

A:

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: We will solve the exponential model for the Aspirin decay

Q: Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18%…

A: Given: Initial population of cockroaches = 3.5 millions = 3500000  Rate of decrease = r=18%=0.18…

Q: A student is 25 years old and the world has a population of 6.2 billion. Assuming that the…

A: Given,  Student's current age = 25 Student's future age = 68 Time (t) = 68 - 25  = 43 Annual growth…

Q: The half-life of a substance is 1200 years. If the initial amount of the substance is 300 grams,…

A:

Q: A bacterial population has an exponential growth rate of 11.2% per hour. If there were 480 bacteria…

A:

Q: The count in a bacteria culture was 600 after 20 minutes and 1700 after 40 minutes. Assuming the…

A:

Q: suppose the half-life of caffeine in the bloodstream of a healthy adult is 6 hours. If the person…

A: Given: initial quantity of caffeine C0=200 mgt=12 hrs (11 am to 11 pm)half life t12= ln 2K…

Q: There were 100 grams of a radioactive substance ten years ago, now there are only 32 grams. Then,…

A: Here we have to find the half-life time.

Q: The count in a bacteria culture was 100 after grows exponentially, What was the initial size of the…

A: Consider the function with exponential growth and the given conditions. a=aoektwhere, ao=initial…

Q: The count in a bacteria culture was 500 after 20 minutes and 1700 after 30 minutes. Assuming the…

A:

Q: A bird species in danger of extinction has a population that is decreasing exponentially A = A0ekt.…

A: Given A=A0ekt Initial population = 1400 when t = 0 after 5 years population is 1000

Q: The size of a threatened population of bottlenosed dolphins is decaying exponentially with a…

A: topic - exponential function

Q: Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The…

A: Given:    Since we have given that Number of bacteria initially = 1   It triples in number every 30…

Q: A bird species in danger of extinction has a population that is decreasing exponentially (A =…

A: NOTE:- YOU HAVE ASKED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU…

Q: What is the half-life of tritium, which decays at a rate of 5.471% per year.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A quantity with an initial value of 980 decays exponentially at a rate of o.3% every decades. What…

A:

Q: The count in a bacteria culture was 500 after 20 minutes and 1100 after 40 minutes. Assuming the…

A:

Q: Emma invested $630$630 in an account in the year 1997, and the value has been growing exponentially…

A: for growing exponentially

Q: After a large number of drinks, a person has a blood alcohol level of 120 mg/dL (milligrams per…

A:

Q: suppose a study is completed that finds that the number of cockroaches in chandler decreases by 18%…

A: Given: Initial population of cockroaches = 3.5 millions = 3500000  Rate of decrease = r=18%=0.18…

Q: If a Paramecium is about 390 micrometers long, how many centimeters is it? Express in real numbers…

A:

Q: The number of women graduating from​ 4-yr colleges in a particular country grew…

A: let the exponential function is   P(t) =P0 ert

Q: The number of bats in a colony is growing exponentially. After 2 years, there were 120 bats. After 5…

A:

Q: If a project takes 10 people 12 months to complete and the Pointy-Haired-Boss says 20 can do it in 6…

A: Given information: 10 people takes 12 months to complete the project. Pointy-Haired-Boss says that…

Q: A cell population grows exponentially beginning with one cell. Which takes longer: increasing from…

A: Definition of the exponential functions helps to find the answer to the problem. A function is said…

Q: The count  in a bacteria culture was 200  after 15 minutes and 1600 40 minutes assuming the count…

A: So we can model the growth of bacteria with an exponential function given by,             f(t)…

Q: Among various populations of plants or animals, diseases spread exponentially. Use the function…

A:

Q: If the generation time is 90 min and the initial population contains 103 cells, how many bacteria…

A:

Q: Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18%…

A: Given information:  Cockroach population decrease by 18% in 12 years.…

Q: A bird species in danger of extinction has a population that is decreasing exponentially (A =…

A: Given population equation - A = A0ekt                ................(1)A0 = Initial Population =…

Q: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

A: A quantity with an initial value of 590 decays exponentially at a rate such that the quantity cuts…

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: Given that the aspirin decays exponentially. Therefore, use the exponential model to find the…

Q: proportional to A, weight W, and height H. A and W measurement values taken from different people…

A:

Q: A culture of 100 bacteria grows to 150 after 2 hours. How long will it take to double in size?…

A: Condition 1: At t=0, P(0)=P0=100   Condition 2: At t=2, P(2)=150   If P(t)=2P0, then find t (in…

Q: An element with a mass of 120 grams decays by 27.5% per minute. What is the exponential equation…

A: Let us suppose that the initial mass of the element is M0 Let the mass after time t minutes be Mt…

Q: The count in a bacteria culture was 300 after 15 minutes and 1800 after 30 minutes. Assuming the…

A: It is given that, Initially, at time t1=15 min. the bacteria count was N1=300 While, at time t2=30…

Q: A quantity with an initial value of 510 grows exponentially at a rate such that the quantity doubles…

A:

Q: A bacteria culture starts with 100 bacteria and grows exponentially, after 1 hour the population is…

A:

Q: The count in a bacteria culture was 400 after 20 minutes and 1000 after 40 minutes. Assuming the…

A:

Q: The population of Brgy. Sta. Isabel starts with 1,000 individuals and triples every 50 years. (a)…

A: Solution:-

Q: A sample of bacteria taken from a river has an initial concentrationof 2.5million bacteria per…

A:

Q: A quantity with an initial value of 390 decays exponentially at a rate of 8.5% every 9 weeks. What…

A: We give the change of the quantity as a function of time as y(t)=390 e-0.0859t where t is in weeks.

Q: A radioactive substance is known to have a half-life of 78 years. Calculate the number of years it…

A:

Q: A biologist is monitoring the population of a rare species of Jackelope. The initial population size…

A:

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: Let the amount of aspirin in bloodstream at time t be N(t) and initial the amount be N0. Therefore…

Q: A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

A: Given:A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.