The number of bacteria P(t) in a certain population increases according to the following function, where time t is measured in hours. P(t)=2400e^0.16t

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: A research group using hospital records developed an approximate mathematical model relating…

A: The rate of change of y with respect to (w.r.t.) is given by derivative of y w.r.t. x i.e., dydx.

Q: a certain culture of organisms grow at a rate proportional to the number present. If it is known…

A:

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

Q: 2. A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a…

A:

Q: A point is moving on the graph of y³ = x². When the point is at (-512, 64), its y coordinate is…

A: Given, A point is moving on the graph of  y3 = x2. When the point is at -512, 64, its y coordinate…

Q: An object is propelled straight up from ground level with an initial velocity of 80 feet per second.…

A: Given that,  s(t) = -16t2 + 80t We have to find t for which s(t)>64

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A: Given query is to find the rate of change of area.

Q: čônčěntrátion enters the tank at 20 kg/min and the mixture leaves the tank after complete mixing at…

A: Given Mass=1000 kg of a 10% salt solution Tinput=2okg/minute→2o% concentration Toutput=1okg/minute…

Q: Average Annual Wage The following table shows theU.S. average annual wage in thousands of dollars…

A: Consider the given table. Now, use the ti-83 calculator to find the function and use the following…

Q: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed…

A: Given that

Q: The rate of growth of profit (in millions) from an invention is approximated by P'(x) =xe x, where x…

A:

Q: A roasted turkey is taken from an oven when its temperature has reached 185° Fahrenheit and is…

A:

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: . The daily amount of smog produced by cars coming into a city is given by y = 2 + 0.01x3/2, where y…

A:

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

A: As population is proportional to present population. So we need to form a differential equation. and…

Q: The value of a brand new car is $36, 000 and the value depreciates 15% every year. Write a function…

A: Please refer to the image below

Q: Suppose that 50,000 bacteria are in a dish and that the population grows continuously by 4% each…

A:

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2…

A:

Q: Element X is a radioactive isotope such that its mass decreases by 57% every hour. If an experiment…

A:

Q: Element X is a radioactive isotope such that its mass decreases by 26% every year. If an experiment…

A: Given that a radioactive element whose mass originally was 490 grams is reduced 26% every year. To…

Q: Element X is a radioactive isotope such that its mass decreases by 82% every year. If an experiment…

A: SOLUTION-

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

A: Given that: Rate of increase of population is proportional to the number of people in the country.At…

Q: The revenue from a manufacturing process (in millions of dollars) is projected to follow the model R…

A:

Q: Between 2006 and 2016, the nurmber of applications for patents, N, grew by about 3.6% per year. That…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 400-cc organ at a rate of 5…

A:

Q: A government agency estimates the number of young adults (ages 18 to 24) in a particular country to…

A: Given that       A Government agency estimates the number of young adults (ages 18 to 24) in a…

Q: The base of a right triangle is decreasing at a rate of 2 meters per hour and the height is…

A:

Q: The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function…

A:

Q: A radioactive substance has a half-life of one week. In other words, at the end of every week the…

A:

Q: A sample of 400 g of radioactive lead-210 decays to polonium-210 according to the function A(t) =…

A:

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That…

A: (a) N'(t)=0.041N(t)dNdt=0.041NdNN=0.041dt∫dNN=∫0.041dtln N=0.041t+celn…

Q: A research was done to study the effect of ambient temperature, x, on the electric power consumed,…

A: Solution

Q: If a ball is thrown into the air with a velocity of 80ft/s, its height in feet after t seconds if…

A: Given y=80t-16t2 ; V=80 ft/SDifferentiate w.r.t 't'dydx=801-162tdydt=80-32tWe know that ,At…

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

A:

Q: can be sold at a price of $p. for  x = cube root of 9,000 - p^4 (close cube root), find the rate of…

A:

Q: When the interest on an investment is compounded continuously, the investment grows at a rate that…

A:

Q: If human toenail grows at an average rate of about 0.13 inch a month.   1 year has 12 months. 1…

A: Given, Growth of human to nail =0.13 inch/month 1 year has 12 months. 1 inch is equal to 2.54 cm.…

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

Q: Element X is a radioactive isotope such that its mass decreases by 87% every year. If an experiment…

A: Decrease by 87%=0.87 per year initial value = 890 grams

Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

A:

Q: On the basis of data for the years 1911 through 1991, the expected life span of people in a country…

A: First find the number of years x from 1908 to date of birth of the person 1966 than put that x in…

Q: On the basis of data for the years 1911 through 1994, the expected life span of people in a country…

A: f(x) = 12.469 lnx +17.128x is the number of years from 1906 to person's birth year.expexted life…

Q: What is the average rate of change of f(x)=log2x from 8 to 32. what is the equation of the seant…

A:

Q: A culture of bacteria initially contains 1200 strands. If the rate of increase in the population of…

A: Equation that formulates the growth is as follows. Pt=P0ektPt is the population after t minutesP0 is…

Q: If we have a formula giving the cholesterol level of a patient as a functionof time, how can we find…

A: Integration gives the function whose derivative is given. Integration means adding all slices to…

Q: trontium-90 is a radioactive isotope that can be produced using nuclear fission, and has a half-life…

A:

Q: The number of daily sales of a product was found to be given by S = 800xe−x2 + 800 x days after the…

A:

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: given that G=cN0.77

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.