A colony of rats is transplanted into an island environment by stowing away on a cargoship. The initial population is 250 and it grows with a doubling time of 8 months. Assumingthat the growth rate stays constant, what will the population be in 5 years?

Q: The rabbit population at the city park increases by 9% per year. If there are initially 289 rabbits…

A:

Q: Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already…

A: given: Initially, there are 1 million bacteria present in a Petri dish.  After 2 minutes, there are…

Q: if the population of Palestine is 6 million in 2020  with a growth rate of 3%/yr when it is expected…

A: Given: The population of Palestine is 6 million in 2020  with a growth rate of 3%/yr

Q: Suppose a man is 30 years old and would like to retire at age 60. Furthermore, he would like to have…

A: In the question  it is asked to calculate the amount of money that a person would save in order to…

Q: A population is exhibiting geometric growth and contains 50 individuals in the initial generation…

A: Introduction: An exponential growth occurs when a fixed number is raised to x, but a geometric…

Q: A certain bacterium is known to grow according to the Malthusian model, doubling itself every 8…

A:

Q: A bacteria population grows by 10% every 3 days. Based on this, if we initially have 2,000…

A: First of all we should know that the growth is exponential so formula will be: Nd = N0ekd where N0…

Q: A population of mosquitoes increases at a daily rate of 1/2 times the current population. You can…

A: Given that A population of mosquitoes increases at a daily rate of 1/2 times the current population.…

Q: The initial population of a town is 3200​, and it grows with a doubling time of 10 years. What will…

A: We have to solve

Q: If a piece of charcoal made from wood of a tree shows only 62% of the carbon 14 expected living in…

A:

Q: The count in a bateria culture was initially 300, and after 35 minutes the population had increased…

A: Given  Initially the count in a bacteria culture = 300 after 35 minutes the population had increased…

Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: Given,initial kangaroo number, n(0) = 200number of kangaroo after 3 years, n(3) =500carrying…

Q: A saving account deposit of $150 is to earn 6.5% compounded continuously. What amount should have…

A: Use the formula for the compound interest and substitute the given values than simplify.

Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: Given:    Half-life of radioactive cobalt =5.27 years    The proportion p that remains after y years…

Q: Total reserves for a non renewable resource at 250 million tones.annual  consumption, currently at…

A: We have total non renewable resources=250 million tonesfirst year consumption is 20 millionsecond…

Q: A certain drug is eliminated from the bloodstream with a​ half-life of 34 hours. Suppose that a…

A:

Q: At current growth rates, the earth’s population is doubling about every 69 years. If this growth…

A: Number  of years - To calculate

Q: population doubles in size every 29 years assuming exponential growth, find the a. annual growth…

A:

Q: An initial population of 8,000 decays for two years until the population is 500. By what percentage…

A: Given-  An initial population of 8,000 decays for two years until the population is 500. To…

Q: If a country experiences a doubling time of 45 years with a growth rate of 1.5%, then we can infer a…

A:

Q: Savannah is going to invest $220 and leave it in an account for 12 years. Assuming the interest is…

A: We have, Savannah is going to invest $220 and leave it in an account for 12 years and at the end,…

Q: If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink. Iodine 131…

A: Given:- If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink.…

Q: 2.A mold population is growth at 8% every three months. If there is initially 3 cubic centimeters of…

A: Formula : Population Growth: P=Po(1+r)n r= rate of growth Po =initial value P= present Value n= no…

Q: The initial population of Sim City is 103 residents, and it grows with a doubling time of 2 hours.…

A:

Q: At time t years an industry consumes fuel at the rate of /(2t + 9) million barrels per year. If the…

A: Linear equation are those equation in which highest power of the variable is 1. The linear equation…

Q: An initial amount of $1800 is invested in an account at an interest rate of 3.5% per year,…

A: givenP=$1800r=3.5%=0.035t=7 yearssince we are solving compouded continuously ,then we apply this…

Q: The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000…

A: Given:The initial number of mosquitoes is 1000. That is, P0 = 1000.The numbr of  mosquitoes is 1600…

Q: An engine health monitoring system consists of a primary unit and a standby unit. The MTTF of the…

A:

Q: Due to the large number of human tourists and a declining food supply, the blue-footed booby…

A: a) Given that the half-life = 13.7 years So the fraction of the booby population that will remain in…

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

A:

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Exponential decay formula: - The amount drops gradually, followed by a quick decrease in the rate of…

Q: City A has a current population of 500,00 people and grows at a rate of 3%/year. City B has a…

A: Given  City A :-  current population(P) is  500,00 people and growth rate (r) is 3% or 0.03  City B…

Q: The population of a city is 89​,000. If the population grows continuously by 3.2​% per​ year, in how…

A:

Q: the number of bacteria in a certain population increases to a continuous exponential growth rate,…

A: NOTE: Refresh your page if you can't see any equations. . the given growth rate is  r=6.2%=0.062

Q: half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Given query is to find the the time taken to reduced the substance to 10 mg.

Q: alf-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only…

A:

Q: A city with a 2010 population of 98,000 has a growth control policy that limits the increase in…

A: The population and the respective years for different annual growth rates are tabulated below. We…

Q: A population with a growth rate equal to zero is

A: The nature of the pop. of a particular area to increase with respect to time is defined as…

Q: The​ half-life of polonium is 139​ days, but your sample will not be useful to you after 91​%of the…

A:

Q: The half-life of Fermium-253 is 3 days. If a sample initially contains 100 mg, how many milligrams…

A: Half-life Formula: Where,  N(t) = amount left after time t                N0 = Initial amount…

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

A:

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

Q: The population of certain species of bats doubles every five hours, initially there are 40 Båts (a)…

A: General formula for exponential growth is given by P(t)=P0ert. Since initially there are 40 bats…

Q: 2. The population of a suburb doubled in size in an 18-month peri growth continues and the current…

A: In this question we will use basic of calculus i.e application of differential equation. We will…

Q: . Use the variation of parameters formula together with the exponential from part 3) to find the…

A: As per the question we have the following second order linear non-homogeneous differential equation…

Q: In the year 2000, the population of a certain country was 285 million with an estimated growth rate…

A: Initial population, P0 = 285 million Growth rate, r = 0.5% = 0.005 Use the exponential growth…

Q: A lake is initially stocked with 400 fish and in the first year the population tripled in size. a)…

A:

Q: The initial population of Rachtropolis is 3100 and it grows with a doubling time of 10 years.…

A:

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.