In Germany the rate of change of a population with respect to time (in years) is proportional to the population. In the year 2000 the population of the country was 100 million. In the year 2010 the population of the country was 115 million. Based on this information, predict the population in the year 2050 accurate to the nearest million. How long (nearest year) will it take for the population to triple

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

A: Here, initial mass =50 mg rate is proportional to the amount.m=50e-0.053t dmdtαm

Q: 4. If the population of a country doubles in 50 years, in how many years will it triple under the…

A: Solve the given for the timing of triple population

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

A:

Q: After 2 hours, the population of a culture of bacteria has increased by 50%. If the rate of growth…

A:

Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

A:

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

A: Explained below

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

A:

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

A:

Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

A:

Q: A certain bacteria culture is observed to double its amount after 150 minutes it was initially…

A: It is given that; let current amount of population is =N The rate of growth of culture is ∝ (N)2…

Q: The population of a city doubles in 50 years. How many years will it be four times as much? Assume…

A:

Q: Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model…

A: Modeling a given set of data in 2 variables is the process of finding the expression relating the…

Q: certain culture of bacteria, the rate of increase is proportional to the numberpresent. (a) If it is…

A: (a) Consider y as the number of bacteria at time t and the rate of change of bacteria can be written…

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A: Solution

Q: Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model…

A:

Q: Consider the constant rate of decrease of a certain microorganism. At the start, there are 50000…

A: Given query is to find the population of microorganisms after 50 second.

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

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: The rate of change of the male population of a particular barangay is proportional to the male…

A:

Q: The velocity v of a falling object is directly proportional to the time t of the fall. If, after 2…

A: What will its velocity be after 3 seconds?

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

A: Given:  If the growth rate of a culture of bacteria is proportional to the number of bacteria…

Q: Initially 42 grams of radioactive substance was present. After 5 hours the mass had decreased by 8%.…

A: Initial mass of radioactive substance is equals to 42 g after five  hours mass is decreased by 8%

Q: A population of 1000 students are in a dormitory. If initially, a virus infected 25 of them. If the…

A: Let number of students infected at time t be x  Then, number of healthy students at time t = (1000 -…

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

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: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We will find in how many year the population of country will be five times as shown below

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

A:

Q: The population of country doubles in 100 years. How many years will it be five times as much? Assume…

A: Denote T as the total population of the country, denote S as the initial population in the country…

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: Suppose an unknown radioactive substance produces 800 counts per minute on a Geiger counter at a…

A:

Q: According to one simplified model, the purchasing power of a dollar in the year 2000 + t is equal to…

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

A:

Q: The population of Barangay Siksikan is increasing at a rate of proportional to its current…

A: given: The population of Barangay Siksikan is increasing at a rate of proportional to its current…

Q: Given the model y=3.2(2.4)^x, what is its rate of change?

A:

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A: Let y be the unconverted amount of substance A at time t. Thus, the given information can be written…

Q: 3. In a certain culture, the rate of growth of bacteria is proportional to the amount present. If…

A:

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We can find the answer as below.

Q: Solve the following: 1. In a certain culture of bacteria, the rate of increases is proportional to…

A: Let the number of bacteria present be x, then the rate of increase is given by x'(t). According to…

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A:

Q: The population of the United States was 3.9 million in 1790 and 178 million In 1960. If the rate of…

A: Given,           The population of the United States was 3.9 million in 1790 and 178 million in…

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…

Q: A puppy weighs 2.0 lb at birth and 3.5 lb 2 months later. If the weight of the puppy during its…

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.