4. In a culture of yeast, the amount of active ferment grows at a rate proportional to the amount present. If the amount doubles in 1 hour, how many times the original amount may be anticipated at the end of 2.75 hours.

Q: 4. Radium decomposes at a rate proportional to the amount present. If half the original amount…

A: Solve differential equation

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: The population of a certain community is known to increase at a rate proportional to the number of…

A:

Q: 6. The population of a community is known to increase at a rate proportional to the number of people…

A: We have to find the time it takes for the population to quadraple.

Q: d) A population of 100 bacteria decays at a rate of 5% each day How many bacteria, y, will there be…

A:

Q: If the population of the earth was found to be 3.5 billion in 1970, and Is Increasing at a rate of…

A: The population of the earth was 3.5 billion in 1970,  We are to find at what year population of…

Q: The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a…

A:

Q: 3. The rate at which radioactive nuclei decay is proportional to the number of such nuclei that are…

A:

Q: 1. U.S. oil reserves are estimated at 29 billion barrels, and we currently produce about 6 MBPD. How…

A: Given  Oil reserves =29 billion barrels 1 billion = 1000million  Current production= 6 million…

Q: 2. The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: A(t) = amount remaining in t years          = A0ekt, where A0 is the initial amount and k is a…

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Suppose…

A: I have appended the formula used in the solution part.

Q: (4) If the population of bacteria in a certain region triples in 50 days. In how many days will be…

A: Assuming the rate of increase is proportional to the number of inhabitants. To find- No. of days in…

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: If the population of bacteria in a certain region triples in 30 days. In how many days will be three…

A:

Q: 2. For a period of time, an island's population grows at a rate proportional to its population. If…

A: Let A0 be the initial population and k be the growth rate.A0 = 1174k = 6.5%  = 0.065

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Let initial population P0Population at time t is P.

Q: 3. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of…

A: Given: initial mass of Radium  y0=96 mgWe know that General decay equation is y=y0e-kt…

Q: 1. The number of a certain type of bacteria increases continuously at a rate proportional to the…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: The population of a certain state is known to grow at a rate proportional to the number of people…

A: Given that 10 years the population has trembled and for  20years the population is 150000. p(t)…

Q: Suppose an unknown radioactive substance produces 22400 counts per minute on a Geiger counter at a…

A:

Q: 3. The population of a certain country is known to increase at a rate proportional to the number of…

A:

Q: The radioactive isotope lead has a half-life of 3.3 hours and decays at a rate proportionate to the…

A: This is a problem of differential equation and integration. Based on the given scenario first of all…

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: Hello! I need help with this particular question on my study guide. There is an attachment below.…

A: Here we use half-life to calculate the exponential decay:

Q: It is known that the population of a certain country at time t is proportional to the people living…

A: Given:- It is known that the population of a certain country at time t is proportional to the people…

Q: 3. If a radioactive substance is quickly decaying at a rate of 13% per hour approximately how much…

A:

Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

A:

Q: 2. Suppose that a bacteria population is dying off at a rate of 30% per day. How much of the…

A:

Q: 5. A storage battery discharge at a rate which is proportional to the charge. If the charger is…

A: Given that: Rate of discharging is proportional to the charge.Charge is reduced to 50% of its…

Q: 1. A body at 50 degrees C cools inside a room with temperature of 30 degrees C. At what temperature…

A: Let's find.

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: 1. For a certain radioactive element decays at a rate of 37.7% per day (tis measured in days). How…

A: We need to find time.

Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Topic:-  exponential function

Q: (4) If the population of bacteria in a certain region triples in 15 days. In how many days will be…

A: Bacteria increases proportional during the period given in the problem

Q: If the world's population grows at a rate proportional to the present population and it is recorded…

A: 20 billion population reached in 2121. Hence correct option is second one. For details calculation…

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: Solved below

Q: Consider 250g of iodine which decomposes at a rate proportional to the amount present. Around 150g…

A: According to the company guidelines only first three 3 subparts will be answered in case of multiple…

Q: In one experimental study, the growth of a certain insects is increasing at a rate proportional to…

A: Given: The growth of insects is increasing at a rate proportional to the number present. To Find:…

Q: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass.  Then  N= No - 25100 No = No - No4=34NoHence    t…

Q: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a…

A:

Q: 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard's average…

A: Given: a) A lizard accelerates from 2 m/s to 10m/s in 4 seconds. What is lizards average…

Q: 4. If caffeine has a half-life of 2 hrs., how many of 140 mg of caffeine remain in Mr. Moreno's…

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.