An endangered species of fish has a population that is decreasing exponentially. The population 5 years ago was 1800. Today, only 800 of the fish are alive. Once the population drops below 100, the situation will be irreversible. When will this happen?

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: The count of bacteria in a culture was 600 after 20 minutes and 2000 after 35 minutes.

A: 20,600 and 35,2000 Let the exponential model be y=abx. Substitute the given point to obtain the…

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: After a large number of drinks, a person has a blood alcohol level of 140 mg/dL (milligrams per…

A: To calculate: the time for the person's blood alcohol level to decrease to 20 mg/dL Given:Initial…

Q: A few weeks into the deadly SARS epidemic in 2003, the number of cases was increasing by about 4%…

A:

Q: The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2…

A:

Q: About the size of New Jersey, Israel has seen its population soar to more than 6 million since it…

A:

Q: The population of Aarb and the population of Bullm are each growing exponentially. In the year 2000,…

A:

Q: Piper invested $900 in an account in the year 2009, and the value has been growing exponentially at…

A:

Q: The value of an investment is increasing exponentially. In year one the investment was 1500 and this…

A:

Q: The population of rabbits on an island is growing exponentially. In the year 2001, the population of…

A: please see the explanation below

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: After 245 years half of a sample of radioactive element remains. Write the equation for modeling its…

A: First form the differential equation than solve it.

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: This year there were 25,000 new births in a large county, but new births are expected to decay…

A:

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

A:

Q: In the year 2006, the age-adjusted death rate per 100,000 Americans for heart disease was 238.5. In…

A: (a) Let exponential model for the given data will be, Dt=D0e-λt, where Dtis death rate 100,000…

Q: A certain tranquilizer decays exponentially in the bloodstream and has a half-life of 45 hours. How…

A: LetA0=100h=45 hrsA(t)=93We know thatA(t)=A0(12)th 93=10012t45Taking ln on both…

Q: Because of an economic slump, a company finds that its annual profits have dropped from 700 thousand…

A: First we shall find profit function with setting intial time 2006

Q: The population in a small town in 2010 was 45,230 people and is growing exponentially at a rate of…

A: Given: The population of the town in 2010 was 45,230. rate of growth is 2%. An exponential growth…

Q: After a large number of drinks, a person has a blood alcohol level of 140 mg/dL (milligrams per…

A: Given:Initial blood alcohol level is 140 mg/dL             And one fourth is removed every hour To…

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

A: To find out the population after 9 months.

Q: The initial size of a bacteria culture that grows exponentially was 10,000. After 1 day, there are…

A:

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: The City of Dallas had a population of 1,270,000 in 2010, and a population of 1,560,000 in 2020. It…

A: According to question given thatThe city of Dallas had a population of=1,270,000 in 2010And a…

Q: In the year 1998, the age-adjusted death rate per 100,000 Americans for heart disease was 235.9. In…

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Q: You decide to invest $250 in an account that yields a return of approximately 4% each year. If yo…

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Q: Suppose the population of spiders in a sanctuary grows exponentially. After one day, 
there were 50…

A:

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: The small intestine bacteria, while inhabiting areas optimal for growth, have a doubling time of…

A: The exponential growth can be studied using the exponential growth function. The formula for the…

Q: The number of bats in a colony is growing exponentially. After 1 year, there were 70 bats. After 4…

A:

Q: The value of a savings bond is growing by 2.8% per year compounded continuously. At this growth…

A:

Q: There are currently 12 frogs in a (large) pond. The frog population grows exponentially, tripling…

A: Given that the frog population grows exponentially, tripling every 6 days. and initial population…

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

A:

Q: The drug Valium is eliminated from the bloodstream exponentially with the half-life of 36 hours.…

A: Given,

Q: A radioactive substance decays exponentially. There are 400 milligrams of the substance to begin…

A:

Q: The population in Littleton in 2010 was 45,300 people and is growing exponentially at a rate of 3%…

A:

Q: A lab culture initially contains 500 bacteria. Two hours later, the number of bacteria decreases to…

A: Given: B(0)  = 500, B(2) = 200, B = B0akt

Q: For a certain patient, a dose of Acetaminophen decays exponentially in their blood stream with a…

A:

Q: Sales of portable MP3 players grew approximately exponentially from ​$0.05 billion in 1999 to ​$0.60…

A:

Q: The count in a bacteria cculture was 300 after 15 minutes and 1800 after 35 minutes. Assuming the…

A:

Q: The median household income (adjusted for inflation) in Seattle grew from $42,500 in 1990 to $75,200…

A:

Q: About the size of New Jersey, Israel has seen its population soar to more than 6 million since it…

A: From the graph, it is given that the population of Palestinians in the West Bank, Gaza strip and…

Q: In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Solve,…

A: Given: In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million

Q: Due to the rising temperatures in a bay ecosystem, the population mass of a certain species of…

A: We have given x(0)=600 tonsx(11)=2,000 tons population increase at…

Q: At the beginning of an experiment, there are 100 bacteria. If the bacteria follow an exponential…

A: At the beginning of an experiment, there are 100 bacteria. If the bacteria follow an exponential…

Q: Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon…

A: Given; A=Ao e^(-0.0001213)

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.