In a chemical reaction, a certain compound changes into another compound at a rate proportional to the unchanged amount. There is 40 grams of the original compound initially and 35 grams after 1 hour. When will 75 percent of the compound be changed?

Q: If a population is recorded at 1,200 in the year 2000 and the rate of increase is a steady 50 people…

A: Given date  Initial population Po=1200 in the year 2000 (t=0) Rate of increase is a steady =50…

Q: After 15 years, one fourth of the initial mass of radioactive substance has decayed. b) Evaluate the…

A:

Q: The number of insects in a colony is known to multiply at a rate proportional to the number of…

A:

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given, the population of a certain country has grown at a rate proportionalto the number of people…

Q: 2. In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Solution is given below:

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

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

A:

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

A: This question is related to the population growth, We will solve it using integration.

Q: In a certain culture of bacteria the rate of increase is proportional to the number present. a. If…

A: Explained below

Q: Suppose that during the first year after its hatching, the weight of a duck increases at a rate…

A: Solution

Q: If the growth rate of a culture of bacteria is proportional to the number of bacteria present. After…

A:

Q: The population of a certain municipality increases at the rate proportional to the present…

A: Here we solve the given population growth problem.

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: The population of an island grows at a rate proportional to its population. If the growth rate is 5%…

A:

Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: A population of bacteria grows at a rate proportional to the number of bacteria at the time. There…

A: Given that:                      Bacteria growth rate is proportional to the number of bacteria at…

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: A certain radioactive material loses mass at a rate proportional to the mass present. If the…

A:

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

A:

Q: In a city with 500,000 population, the rate of the spread of a new flu epidemic is proportional to…

A:

Q: An amplifire is having a gain of 500 without feedback.If negative feedback is applied.the gain is…

A: Given:    Av   =  500    Avf   = 100

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

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Initially 50 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A: The rate of change of amount A with respect to time t can be denoted by dAdt. If x is directly…

Q: A certain type of bacteria is known to grow at the rate proportional to square root of the amount…

A: To find- how much bacteria is there after 7 hours.

Q: Bacteria grown in a certain culture increase at a rate proportional to the amount present. If there…

A: This question is based on application of diffrential equation.

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A:

Q: The substance decomposed at a rate proportional to the amount resent. What is the half-life of the…

A:

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

Q: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

Q: If the price of gold decrease at a monthly rate of 2.1%, by what percentage does it decrease in a…

A: If something is decreasing at 2.1% per month,then after 1 month we have 100%-2.1%=97.9%so after each…

Q: The population of Tagum City is increasing at the rate proportional to its current population. In…

A:

Q: The population of a district in a town is known to increase at a rate proportional to the number of…

A: We will find out the required initial population of the state .

Q: The half-life of radioactive strontium-90 is approximately 29 years. In 1965, radioactive…

A:

Q: A certain population of bacteria doubled after 20 minutes. If it is known that it grows proportional…

A:

Q: Radium decomposes at a rate proportional to its present radioactive. In 100 years, 100 units of…

A:

Q: If the growth rate of a culture of bacteria is proportional to the number of bacteria present and…

A:

Q: The number of children in a church is increasing at a rate that is proportional to the number of…

A: We will find the number of children after 5 years as following.

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

A:

Q: In a certain bacteria culture the rate of increase in a number of bacteria proportional to the…

A:

Q: * Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70…

A:

Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

A:

Q: The half-life of radioactive strontium-90 is approximately 27 years. In 1963, radioactive…

A:

Q: Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70 kg…

A: The amount of sugar present initially is 70 kg and at the end of 4 hours only 30 kg is left. The…

Q: The population of an endangered species decreases at a rate of 7% per year. Approximately how long…

A: Answer

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: Radium decomposes at a rate proportional to the amount present. In 100 yrs, 100 mg of radium…

A: Initial radium quantity Ni = 100 mg after t = 100 years N = 96 mg

Q: A certain mold grows at a rate proportional to its present size. If the original amount doubles in…

A: Given that a certain mold grows at a rate proportional to its present size. And the original amount…

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.