According to a particular model for predicting the height of preschool children, the rate of growth of a typical preschool child is R(t) = 25.395e-0.984t + 5.42 (sts 6) centimeters/year, where t is measured in years. The height of a typical 3-month-old preschool child is 55.7000 cm. (a) Find a model for predicting the height of a typical preschool child at age t. (Round numerical values to four decimal places.) H(t) = (b) Use the result of part (a) to estimate the height of a typical 1-year-old child. (Round your answer to two decimal places.) cm

Q: Five mice in a stable population of 500 are intentionally infected at r= 0 with a contagious disease…

A:

Q: A sample population of strands of the bacteria is increasing at rate proportional to the population.…

A:

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: Given An environmentalist find that a certain types of tree grows in such a way that its height h(t)…

Q: An inverted cone has a diameter of 9m, height of 12m and at t= 0, is 87.5% full of water. At that…

A: Here the Torricelli's law is to be used. The Torricelli's law states that the rate of change of…

Q: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides…

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from…

Q: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: Given: The trough is being filled with water at the rate of 0.3 m3/min, dVdt=0.3 m3/min

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

A:

Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

A: Given the rate of change= 0.6+4/(t+2)2 feet per year To find the total number of feet grown during…

Q: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

Q: 11. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A:

Q: A man of height  1.9  meters walks away from a 5-meter lamppost at a speed of  2.1  m/s. Find the…

A: Let distance of the man from the pole=x   Let the length of the shadow =y…

Q: 6) A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

A:

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

A:

Q: 2. A street lamp is 5m tall and located 6m from a brick wall. A person who is 2m tall walks away…

A:

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

Q: Initially there was 80 milligrams of radioactive substance present.  After an 8 hour period the mass…

A: From the differential equation from the given information. dPdt=kPdPP=kdt Here, the amount of…

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: A trough is 2 meters long and a cross-section has the shape of an isosceles trapezoid that is 20 cm…

A: Use volume of trapezoid

Q: Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that…

A:

Q: At 12-ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

A: A) Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

A:

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

Q: Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that…

A:

Q: A culture initially has No number of bacteria. At t =1hours the number of bacteria is measured to be…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: Given Data: The height of the man is: h=1.9 m The height of the lamppost is: H=5 m The increasing…

Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

A:

Q: projected that, t months from now, the population of a certain town will be growing at the rate of…

A:

Q: Based on the data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

A:

Q: The length of a rectangle is decreasing at the rate of 5 cm/s and its width is increasing at the…

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A: Make a diagram according to the situation.

Q: A tank contains 400L of fresh water. By mistake, 100kg of salt is poured into the tank instead of…

A:

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: The volume of water trough = Area × Length Area of trapezium = 12×Sum of parallel sides×height…

Q: 6) A light is 20 meters above a straight horizontal path. If a man 1.65 meters tall is walking away…

A: Given: Height of light is 20 meter. Height of man is 1.65 meters. Rate with which man is walking is…

Q: Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that…

A: Now given that

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

A:

Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 2800 f(t) : (æ +…

A:

Q: A 50-gallon tank initially contains 10 gallons of fresh water. At t= 0, a brine solution containing…

A: We will find out the required time.

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x…

A: Given: The total net shipments of aluminum (in billions of pounds) are approximated by…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.