A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below, where t is the time in hours measured from 5:00 AM. What is the total basal metabolism of this man over a 24 hour period? R(t) = 95 – 0.18cos = 2260 x kcal

Q: 2. A stone is dropped from the upper observation deck of the CN Tower, 450 meters above the ground.…

A: As you asked too many question , I only answered first three

Q: A radioactive substance decays according to the equation N = 105 e SIA where N is the number of…

A:

Q: A ball is thrown from an initial height of 6 feet with an initial upward velocity of 17 ft/s. The…

A: The roots of a quadratic equation are the values of the variable for which the value of the equation…

Q: According to a particular model for predicting the height of preschool children, the rate of growth…

A: Given  Rt=25.907e-0.983t+5.12

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

A:

Q: The rate of increase of the population of a certain city is proportional to the population. In 1970,…

A:

Q: The cost of certain piece of machinery is $ 700 and its value is depreciating with time according to…

A: We have to find the value after 6 years.

Q: radioactive isotope decays in such a way that the number of atoms present ven time, N(t), obeys the…

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A: We have to solve the differential equation as a function of t.

Q: A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following…

A:

Q: The doubling period of a bacterial population is 10 minutes. At time t = 120 minutes, the bacterial…

A: Given:The doubling period of a bacterial population is 10 minutesAt t=120 minutes , bacterial…

Q: A population of fish is modeled by the equation dP/dt = .00016P(1300-P)+20 with an initial…

A: Roots of quadratic equation Plotting of graph of Quadratic equation with the help of roots. Basic…

Q: A population of 500 bacteria is introduced into a culture and grows in number according to the…

A: Given: pt=5001+4t50+t2 we know that population growing rate is given by differentiation of given…

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

A:

Q: A certain radioactive substance decays according to the formula q(t) = q0e −0.0031t where q0 is the…

A: The radioactive substace decay equation is given byq(t)=q0e-0.0031t.........(1)where q0is the…

Q: The rate of growth, dP/dt of a population of bacteria is given by dP/dt=k sqrt of t, where P is the…

A:

Q: The population of a colony of bacteria is modeled by the function P(x) = 50(e-X -e-*") + 10, for 0 <…

A:

Q: The air in a room with volume 180 m3 contains 0.2% carbon dioxide initially. Fresher air with only…

A: Given : Room volume = 180 m³ which initially contains 0.2% carbon dioxide

Q: The number of cells in a bacteria population is given by P(t) = 1200 - 2 where t is measured in…

A: The number of cells in a bacteria population is given by, Pt=12002t

Q: A sample of 500 g of radioactive​ lead-210 decays to​ polonium-210 according to the function…

A: Given function  A(t)=500e−0.032t Here, A(t) is the amount of radioactive lead and t is the time in…

Q: THe model for the growth rate of tumor known as the Gompertz Tumor Growth is given by the following…

A:

Q: ) When an object is removed from a furnace and placed in an environment with a constant tem-…

A:

Q: Find a formula for P=f(t), the size of the population that begins in year t=0 with 2,420 members and…

A: In the given problem we have to find out the general formula for decay of size of population as a…

Q: A radio active element (x) has a half-life of 38 hours. Initially, X = X0 %3D . Determine the amount…

A:

Q: The air in a room with volume 180 m3 contains 0.15% carbon dioxide initially. Fresher air with only…

A:

Q: While doing battle with Krang in Dimension X, Raphael was exposed to a radioactive cloud. Three…

A:

Q: Starting with an initial value of P(0)=55, the population of a crow community grows at a rate of…

A:

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: The air in a room with volume 180 m³ contains 0.3% carbon dioxide initially. Fresher air with only…

A:

Q: The doubling period of a bacterial population is 10 minutes. At time t = 100 minutes, the bacterial…

A:

Q: Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A: Here,Boyle's law is given  PV = C  By differentiation with respect to time we can find change in…

Q: According to a particular model for predicting the height of preschool children, the rate of growth…

A: Given,Rate of growth of a child, R(t) = 24.348 e-0.993t+ 6.41  cm/yr    t∈ (0.25,6)Height of child…

Q: The population of a certain inner-city area is estimated to be declining according to the model…

A: Given: The population decline of a certain city is given as, P(t)=580000e-0.022t t- Number of years…

Q: A population of insects increases at a rate of 20010t 0.25t2 insects per day 3. (t in day units).…

A: It is given that initially there are 35 insects at t = 0. So, I (0) = 35.

Q: A mathematical model for population growth over short intervals is given by P=P0ert​, where P0 is…

A:

Q: At the beginning of an experiment, a scientist has 352 grams of radioactive goo. After 225 minutes,…

A: Let the formula of G(t) is, Gt=G0e-kt

Q: Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A: Consider the given equation: PV=CV=600 cm3P=80 kPadPdt=20 kPa/min Differentiate PV=C with respect to…

Q: The doubling period of a bacterial population is 10 minutes. At time t = 110 minutes, the bacterial…

A:

Q: Let C(t) be the concentration of a drug in the bloodstream. AS the body eliminates the drug, C(t)…

A:

Q: At the beginning of an experiment, a scientist has 164 grams of radioactive goo. After 105 minutes,…

A: We will solve the following.

Q: After an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood…

A: Consider the given function  Ct=0.135 t·e-2.802 t

Q: A population grows at a rate P'(t) = 500te-0.2t P(t) is the population after t months. What is the…

A: Population growth at a rate P’(t) = 500te-0.2t2 Where P(t) is the population after t months Evaluate…

Q: Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A: Given that:- Boyle's Law states that when a sample of gas is compressed at a constant temperature,…

Q: The population of a certain inner-city area is estimated to be be declining according to the model…

A: Given that t=13  We have to find P(13)

Q: After an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood…

A: Here, the given function is: C(t)=0.135te-2.802t...(1) which models the average BAC, measured in…

Q: A biologist is researching a newly discovered species of bacteria. At time t = 0, he puts 200…

A: (a) Let the initial number of bacteria be a. The number of bacteria at any time t be P(t) and time…

Q: Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of…

A: Given query is to find the volue at time t

Q: According to a particular model for predicting the height of preschool children, the rate of growth…

A:

Q: The air in a room with volume 180 m3 contains 0.1% carbon dioxide initially. Fresher air with only…

A: Let % of CO2 at time t be ptAmount of CO2 in room=volume of room×pRate of change of…

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.